Simplifying Radical Expressions...©Glencoe/McGraw-Hill 658 Glencoe Algebra 1 Solve each equation. Check your solution. 1. Ï2wb 5 8 2. 4Ï3w 5 Ïxw 3. 2Ï4wc 1 3 5 11 4. 6 2 Ï2wy

Skills Practice

Simplifying Radical Expressions

NAME ______________________________________________ DATE ____________ PERIOD _____

11-111-1

© Glencoe/McGraw-Hill 645 Glencoe Algebra 1

Less

on

11-1

Simplify.

1. Ï28w 2. Ï40w

3. Ï72w 4. Ï99w

5. Ï2w ? Ï10w 6. Ï5w ? Ï60w

7. 3Ï5w ? Ï5w 8. Ï6w ? 4Ï24w

9. 2Ï3w ? 3Ï15w 10. Ï16b4w

11. Ï81c2dw4w 12. Ï40x4yw6w

13. Ï75m5nw2w 14. Îã

15. Îã 16. Îã ? Îã

17. Îã 18. Îã

19. Îã 20. Îã

21. 22.

23. 24.4

}

3 2 Ï2w5

}

7 1 Ï7w

3}

2 2 Ï3w2

}

4 1 Ï5w

45}4m4

12}b2

4h}5

q}12

1}3

6}7

1}6

5}3


Simplify.

1. Ï24w 2. Ï60w

3. Ï108w 4. Ï8w ? Ï6w

5. Ï7w ? Ï14w 6. 3Ï12w ? 5Ï6w

7. 4Ï3w ? 3Ï18w 8. Ï27su3w

9. Ï50p5w 10. Ï108x6wy4z5w

11. Ï56m2nw4o5w 12.

13. Îã 14. Îã15. Îã ? Îã 16. Îã ? Îã17. 18. Îã19. Îã 20. Îã21. 22.

23. 24.

25. SKY DIVING When a skydiver jumps from an airplane, the time t it takes to free fall a

given distance can be estimated by the formula t 5 Îã, where t is in seconds and s is in

meters. If Julie jumps from an airplane, how long will it take her to free fall 750 meters?

METEOROLOGY For Exercises 26 and 27, use the following information.

To estimate how long a thunderstorm will last, meteorologists can use the formula

t 5 Îã, where t is the time in hours and d is the diameter of the storm in miles.

26. A thunderstorm is 8 miles in diameter. Estimate how long the storm will last. Give youranswer in simplified form and as a decimal.

27. Will a thunderstorm twice this diameter last twice as long? Explain.

d3

}216

2s}9.8

3Ï7w}}

21 2 Ï27w5

}}

Ï7w 1 Ï3w

8}

3 1 Ï3w3

}

5 2 Ï2w

9ab}4ab4

4y}3y2

18}x3

Ï3kw}

Ï8w

7}11

1}7

4}5

3}4

5}32

2}10

Ï8w}

Ï6w

Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

11-111-1

Reading to Learn Mathematics


NAME ______________________________________________ DATE ____________ PERIOD _____

11-111-1


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11-1

Pre-Activity How are radical expressions used in space exploration?

Read the introduction to Lesson 11-1 at the top of page 586 in your textbook.

Suppose you want to calculate the escape velocity for a spacecraft taking offfrom the planet Mars. When you substitute numbers in the formula, whichnumber is sure to be the same as in the calculation for the escape velocityfor a spacecraft taking off from Earth?

Reading the Lesson

1. a. How can you tell that the radical expression Ï28x2yw4w is not in simplest form?

b. To simplify Ï28x2yw4w, you first find the of 28x2y4.

You then apply the . In this case,

Ï4 ? 7 ?w x2? yw4w is equal to the product . You can simplify

again to get a final answer of 2|x|y2Ï7w.

2. Why is it correct to write Ïy4w 5 y2, with no absolute value sign, but not correct to write

Ïx2w 5 x?

3. What method would you use to simplify ?

4. What should you do to write the conjugate of a binomial of the form aÏbw 1 cÏdw? To

write the conjugate of a binomial of the form aÏbw 2 cÏdw?

Helping You Remember

5. What should you remember to check for when you want to determine if a radicalexpression is in simplest form?

Ï12tw}

Ï15w

Skills Practice

Operations with Radical Expressions

NAME ______________________________________________ DATE ____________ PERIOD _____

11-211-2


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on

11-2

Simplify each expression.

1. 7Ï7w 2 2Ï7w 2. 3Ï13w 1 7Ï13w

3. 6Ï5w 2 2Ï5w 1 8Ï5w 4. Ï15w 1 8Ï15w 2 12Ï15w

5. 12Ïcw 2 9Ïcw 6. 9Ï6aw 2 11Ï6aw 1 4Ï6aw

7. Ï44w 2 Ï11w 8. Ï28w 1 Ï63w

9. 4Ï3w 1 2Ï12w 10. 8Ï54w 2 4Ï6w

11. Ï27w 1 Ï48w 1 Ï12w 12. Ï72w 1 Ï50w 2 Ï8w

13. Ï180w 2 5Ï5w 1 Ï20w 14. 2Ï24w 1 4Ï54w 1 5Ï96w

15. 5Ï8w 1 2Ï20w 2 Ï8w 16. 2Ï13w 1 4Ï2w 2 5Ï13w 1 Ï2w

Find each product.

17. Ï2w(Ï8w 1 Ï6w) 18. Ï5w(Ï10w 2 Ï3w)

19. Ï6w(3Ï2w 2 2Ï3w) 20. 3Ï3w(2Ï6w 1 4Ï10w )

21. (4 1 Ï3w)(4 2 Ï3w) 22. (2 2 Ï6w)2

23. (Ï8w 1 Ï2w)(Ï5w 1 Ï3w) 24. (Ï6w 1 4Ï5w)(4Ï3w 2 Ï10w )


Simplify each expression.

1. 8Ï30w 2 4Ï30w 2. 2Ï5w 1 7Ï5w 2 5Ï5w

3. 7Ï13xw 2 14Ï13xw 1 2Ï13xw 4. 2Ï45w 1 4Ï20w

5. Ï40w 2 Ï10w 1 Ï90w 6. 2Ï32w 1 3Ï50w 2 3Ï18w

7. Ï27w 1 Ï18w 1 Ï300w 8. 5Ï8w 1 3Ï20w 2 Ï32w

9. Ï14w 2 Îã 10. Ï50w 1 Ï32w 2 Îã11. 5Ï19w 1 4Ï28w 2 8Ï19w 1 Ï63w 12. 3Ï10w 1 Ï75w 2 2Ï40w 2 4Ï12w

Find each product.

13. Ï6w(Ï10w 1 Ï15w) 14. Ï5w(5Ï2w 2 4Ï8w)

15. 2Ï7w(3Ï12w 1 5Ï8w) 16. (5 2 Ï15w)2

17. (Ï10w 1 Ï6w)(Ï30w 2 Ï18w ) 18. (Ï8w 1 Ï12w )(Ï48w 1 Ï18w )

19. (Ï2w 1 2Ï8w)(3Ï6w 2 Ï5w) 20. (4Ï3w 2 2Ï5w)(3Ï10w 1 5Ï6w)

SOUND For Exercises 21 and 22, use the following information.

The speed of sound V in meters per second near Earth’s surface is given by V 5 20Ït 1 27w3w,where t is the surface temperature in degrees Celsius.

21. What is the speed of sound near Earth’s surface at 15°C and at 2°C in simplest form?

22. How much faster is the speed of sound at 15°C than at 2°C?

GEOMETRY For Exercises 23 and 24, use the following information.

A rectangle is 5Ï7w 1 2Ï3w centimeters long and 6Ï7w 2 3Ï3w centimeters wide.

23. Find the perimeter of the rectangle in simplest form.

24. Find the area of the rectangle in simplest form.

1}2

2}7

Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

11-211-2



NAME ______________________________________________ DATE ____________ PERIOD _____

11-211-2


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on

11-2

Pre-Activity How can you use radical expressions to determine how far a personcan see?


Suppose you substitute the heights of the Sears Tower and the Empire StateBuilding into the formula to find how far you can see from atop each building.What operation should you then use to determine how much farther you cansee from the Sears Tower than from the Empire State Building?

Reading the Lesson

1. Indicate whether the following expressions are in simplest form. Explain your answer.

a. 6Ï3w 2 Ï12w

b. 12Ï6w 1 7Ï10w

2. Below the words First terms, Outer terms, Inner terms, and Last terms, write the

products you would use to simplify the expression (2Ï15w 1 3Ï15w)(6Ï3w 2 5Ï2w).

First terms Outer terms Inner terms Last terms

1 1 1


3. How can you use what you know about adding and subtracting monomials to help youremember how to add and subtract radical expressions?

Skills Practice

Radical Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

11-311-3


Less

on

11-3

Solve each equation. Check your solution.

1. Ïfw 5 7 2. Ï2xw 5 5

3. Ï5pw 5 10 4. Ï4yw 5 6

5. 2Ï2w 5 Ïuw 6. 3Ï5w 5 Ï2nw

7. Ïgw 2 6 5 3 8. Ï5aw 1 2 5 0

9. Ï2c 2 1w 5 5 10. Ï3k 2w2w 5 4

11. Ïx 1 4w 2 2 5 1 12. Ï4x 2 4w 2 4 5 0

13. 5 4 14. Îã 5 3

15. x 5 Ïx 1 2w 16. d 5 Ï12 2wdw

17. Ï6x 2 9w 5 x 18. Ï6p 2w8w 5 p

19. Ïx 1 5w 5 x 2 1 20. Ï8 2 cw 5 c 2 8

21. Ïr 2 3w 1 5 5 r 22. Ïy 2 1w 1 3 5 y

23. Ï5n 1w4w 5 n 1 2 24. Ï3z 2 6w 5 z 2 2

m}3

Ïdw}

3


Solve each equation. Check your solution.

1. Ï2bw 5 8 2. 4Ï3w 5 Ïxw

3. 2Ï4cw 1 3 5 11 4. 6 2 Ï2yw 5 22

5. Ïk 1 2w 2 3 5 7 6. Ïm 2 5w 5 4Ï3w

7. Ï6t 1 1w2w 5 8Ï6w 8. Ï3j 2 1w1w 1 2 5 9

9. Ï2x 1 1w5w 1 5 5 18 10. Îã2 4 5 2

11. 6Îã 2 3 5 0 12. 6 1Îã 5 22

13. y 5 Ïy 1 6w 14. Ï15 2w2xw 5 x

15. Ïw 1 4w 5 w 1 4 16. Ï17 2wkw 5 k 2 5

17. Ï5m 2w 16w 5 m 2 2 18. Ï24 1w8qw 5 q 1 3

19. Ï4s 1 1w7w 2 s 2 3 5 0 20. 4 2 Ï3m 1w 28w 5 m

21. Ï10p 1w 61w 2 7 5 p 22. Ï2x22w 9w 5 x

ELECTRICITY For Exercises 23 and 24, use the following information.

The voltage V in a circuit is given by V 5 ÏPRw, where P is the power in watts and R is theresistance in ohms.

23. If the voltage in a circuit is 120 volts and the circuit produces 1500 watts of power, whatis the resistance in the circuit?

24. Suppose an electrician designs a circuit with 110 volts and a resistance of 10 ohms. Howmuch power will the circuit produce?

FREE FALL For Exercises 25 and 26, use the following information.

Assuming no air resistance, the time t in seconds that it takes an object to fall h feet can be

determined by the equation t 5 .

25. If a skydiver jumps from an airplane and free falls for 10 seconds before opening theparachute, how many feet does the skydiver fall?

26. Suppose a second skydiver jumps and free falls for 6 seconds. How many feet does thesecond skydiver fall?

Ïhw}

4

5r}6

3x}3

3s}5

Practice

Radical Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

11-311-3


Radical Equations

NAME ______________________________________________ DATE ____________ PERIOD _____

11-311-3


Less

on

11-3

Pre-Activity How are radical equations used to find free-fall times?


How can you isolate Ïhw on one side of the equation?

Reading the Lesson

1. To solve a radical equation, you first isolate the radical on one side of the equation. Whydo you then square each side of the equation?

2. a. Provide the reason for each step in the solution of the given radical equation.

Ï5x 2 1w 2 4 5 x 2 3 Original equation

Ï5x 2 1w 5 x 1 1

(Ï5x 2 1w)25 (x 1 1)2

5x 2 1 5 x21 2x 1 1

0 5 x22 3x 1 2

0 5 (x 2 1)(x 2 2)

x 2 1 5 0 or x 2 2 5 0

x 5 1 x 5 2

b. To be sure that 1 and 2 are the correct solutions, into which equation should yousubstitute to check?

3. a. How do you determine whether an equation has an extraneous solution?

b. Is it necessary to check all solutions to eliminate extraneous solutions? Explain.


4. How can you use the letters ISC to remember the three steps in solving a radicalequation?

Skills Practice

The Pythagorean Theorem

NAME ______________________________________________ DATE ____________ PERIOD _____

11-411-4


Less

on

11-4

Find the length of each missing side. If necessary, round to the nearest

hundredth.

1. 2. 3.

4. 5. 6.

If c is the measure of the hypotenuse of a right triangle, find each missing

measure. If necessary, round to the nearest hundredth.

7. a 5 21, b 5 28, c 5 ? 8. a 5 6, c 5 10, b 5 ?

9. a 5 15, b 5 36, c 5 ? 10. a 5 16, c 5 20, b 5 ?

11. a 5 5, b 5 12, c 5 ? 12. b 5 6, c 5 12, a 5 ?

13. a 5 11, b 5 4, c 5 ? 14. a 5 8, b 5 10, c 5 ?

15. a 5 19, b 5 Ï39w, c 5 ? 16. a 5 Ï12w, b 5 6, c 5 ?

17. c 5 Ï130w, a 5 7, b 5 ? 18. a 5 Ï6w, b 5 Ï19w, c 5 ?

Determine whether the following side measures form right triangles. Justify your

answer.

19. 7, 24, 25 20. 15, 30, 34

21. 16, 28, 32 22. 18, 24, 30

23. 15, 36, 39 24. 5, 7, Ï74w

250

240

a4

9

c

2933

b

1634

b

1539

a

21

72

c


Find the length of each missing side. If necessary, round to the nearest

hundredth.

1. 2. 3.

If c is the measure of the hypotenuse of a right triangle, find each missing

measure. If necessary, round to the nearest hundredth.

4. a 5 24, b 5 45, c 5 ? 5. a 5 28, b 5 96, c 5 ?

6. b 5 48, c 5 52, a 5 ? 7. c 5 27, a 5 18, b 5 ?

8. b 5 14, c 5 21, a 5 ? 9. a 5 Ï20w, b 5 10, c 5 ?

10. a 5 Ï75w, b 5 Ï6w, c 5 ? 11. b 5 9x, c 5 15x, a 5 ?

Determine whether the following side measures form right triangles. Justify your

answer.

12. 11, 18, 21 13. 21, 72, 75

14. 7, 8, 11 15. 9, 10, Ï161w

16. 9, 2Ï10w, 11 17. Ï7w, 2Ï2w, Ï15w

18. STORAGE The shed in Stephan’s back yard has a door that measures 6 feet high and 3 feet wide. Stephan would like to store a square theater prop that is 7 feet on a side.Will it fit through the door diagonally? Explain.

SCREEN SIZES For Exercises 19–21, use the following information.

The size of a television is measured by the length of the screen’s diagonal.

19. If a television screen measures 24 inches high and 18 inches wide, what size television is it?

20. Darla told Tri that she has a 35-inch television. The height of the screen is 21 inches.What is its width?

21. Tri told Darla that he has a 5-inch handheld television and that the screen measures 2 inches by 3 inches. Is this a reasonable measure for the screen size? Explain.

124

b1911

a

60

32c

Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

11-411-4



NAME ______________________________________________ DATE ____________ PERIOD _____

11-411-4


Less

on

11-4

Pre-Activity How is the Pythagorean Theorem used in roller coaster design?


The diagram in the introduction shows a right triangle and part of theroller coaster. Which side of the right triangle has a length approximatelyequal to the length of the first hill of the roller coaster?

Reading the Lesson

Complete each sentence.

1. The words leg and hypotenuse refer to the sides of a triangle.

2. In a right triangle, each of the two sides that form the right angle is a of the right triangle.

3. The longest side of a right triangle is called the of the right triangle.

Write an equation that you could solve to find the missing side length of each

right triangle.

4. 5. 6.

7. Suppose you are given three positive numbers. Explain how you can decide whetherthese numbers are the lengths of the sides of a right triangle.


8. Think of a word or phrase that you can associate with the Pythagorean Theorem to helpyou remember the equation c2

5 a21 b2.

9

106

109

10

Skills Practice

The Distance Formula

NAME ______________________________________________ DATE ____________ PERIOD _____

11-511-5


Less

on

11-5

Find the distance between each pair of points whose coordinates are given.

Express answers in simplest radical form and as decimal approximations rounded

to the nearest hundredth if necessary.

1. (9, 7), (1, 1) 2. (5, 2), (8, 22)

3. (1, 23), (1, 4) 4. (7, 2), (25, 7)

5. (26, 3), (10, 3) 6. (3, 3), (22, 3)

7. (21, 24), (26, 0) 8. (22, 4), (5, 8)

9. (23, 4), (22, 8) 10. (5, 26), (7, 29)

11. (4, 2), (8, 6) 12. (5, 2), (3, 10)

13. (12, 21), (4, 211) 14. (23, 21), (211, 3)

15. (9, 3), (6, 26) 16. (0, 24), (8, 4)

Find the possible values of a if the points with the given coordinates are the

indicated distance apart.

17. (22, 25), (a, 7); d 5 13 18. (8, 22), (5, a); d 5 3

19. (4, a), (1, 6); d 5 5 20. (a, 3), (5, 21); d 5 5

21. (1, 1), (a, 1); d 5 4 22. (2, a), (2, 3); d 5 10

23. (a, 2), (23, 3); d 5 Ï2w 24. (25, 3), (23, a); d 5 Ï5w


Find the distance between each pair of points whose coordinates are given.

Express answers in simplest radical form and as decimal approximations rounded

to the nearest hundredth if necessary.

1. (4, 7), (1, 3) 2. (0, 9), (27, 22)

3. (4, 26), (3, 29) 4. (23, 28), (27, 2)

5. (0, 24), (3, 2) 6. (213, 29), (21, 25)

7. (6, 2), 14, 2 8. (21, 7), 1 , 62

9. 12, 2 2, 11, 2 10. 1 , 212, 12, 2

11. (Ï3w, 3), (2Ï3w, 5) 12. (2Ï2w, 21), (3Ï2w, 3)

Find the possible values of a if the points with the given coordinates are the

indicated distance apart.

13. (4, 21), (a, 5); d 5 10 14. (2, 25), (a, 7); d 5 15

15. (6, 27), (a, 24); d 5 Ï18w 16. (24, 1), (a, 8); d 5 Ï50w

17. (8, 25), (a, 4); d 5 Ï85w 18. (29, 7), (a, 5); d 5 Ï29w

BASEBALL For Exercises 19–21, use the following information.

Three players are warming up for a baseball game. Player B stands 9 feet to the right and 18 feet in front of Player A.Player C stands 8 feet to the left and 13 feet in front of Player A.

19. Draw a model of the situation on the coordinate grid.Assume that Player A is located at (0, 0).

20. To the nearest tenth, what is the distance between Players Aand B and between Players A and C?

21. What is the distance between Players B and C?

22. MAPS Maria and Jackson live in adjacent neighborhoods. If they superimpose acoordinate grid on the map of their neighborhoods, Maria lives at (29, 1) and Jacksonlives at (5, 24). If each unit on the grid is equal to approximately 0.132 mile, how farapart do Maria and Jackson live?

A(0, 0)

B(9, 18)

C(28, 13)

x

y

O 4 8

16

12

8

4

28 24

1}3

2}3

1}2

1}2

1}3

1}2

Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

11-511-5



NAME ______________________________________________ DATE ____________ PERIOD _____

11-511-5


Less

on

11-5

Pre-Activity How can the distance between two points be determined?


What are the coordinates of points A, B, and C?

Reading the Lesson

1. Suppose you want to use the Distance Formula to find the distance between (6, 4) and (2, 1). Use (x1, y1) 5 (6, 4) and (x2, y2) 5 (2, 1). Complete the equations by writing the correct numbers in the blanks.

a. x1 5 y1 5 x2 5 y2 5

b. d 5 Ïwwww( 2 )21 ( 2 )2

2. Suppose you want to use the Distance Formula to find the distance between (3, 7) and(9, 22). Use (x1, y1) 5 (3, 7) and (x2, y2) 5 (9, 22). Complete the equations by writing thecorrect numbers in the blanks.

a. x1 5 y1 5 x2 5 y2 5

b. d 5 Ïwwww( 2 )21 ( 2 )2

3. A classmate is using the Distance Formula to find the distance between two points. She

has done everything correctly so far, and her equation is d 5 Ï(22 2w 5)21w (7 2w11)2w.

This equation will give her the distance between what two points?


4. Sometimes it is easier to remember a formula if you can state it in words. How can youstate the Distance Formula in easy-to-remember words?

x

y

O

A

B

Skills Practice

Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

11-611-6


Less

on

11-6

Determine whether each pair of triangles is similar. Justify your answer.

1. 2.

3. 4.

For each set of measures given, find the measures

of the missing sides if nPQR , nSTU.

5. r 5 4, s 5 6, t 5 3, u 5 2

6. t 5 8, p 5 21, q 5 14, r 5 7

7. p 5 15, q 5 10, r 5 5, s 5 6

8. p 5 48, s 5 16, t 5 8, u 5 4

9. q 5 6, s 5 2, t 5 , u 5

10. p 5 3, q 5 2, r 5 1, u 5

11. p 5 14, q 5 7, u 5 2.5, t 5 5

12. r 5 6, s 5 3, t 5 , u 59}4

21}8

1}3

1}2

3}2

P R

Q

q

r p

S U

T

t

u s

528528

638

658F E H

J

K

G408

408458

F

E G H

JK

608

608

578608

XV

W

U

Z

Y

408

508

A

D F

E

C

B


Determine whether each pair of triangles is similar. Justify your answer.

1. 2.

For each set of measures given, find the measures

of the missing sides if nABC , nDEF.

3. c 5 4, d 5 12, e 5 16, f 5 8

4. e 5 20, a 5 24, b 5 30, c 5 15

5. a 5 10, b 5 12, c 5 6, d 5 4

6. a 5 4, d 5 6, e 5 4, f 5 3

7. b 5 15, d 5 16, e 5 20, f 5 10

8. a 5 16, b 5 22, c 5 12, f 5 8

9. a 5 , b 5 3, f 5 , e 5 7

10. c 5 4, d 5 6, e 5 5.625, f 5 12

11. SHADOWS Suppose you are standing near a building and you want to know its height.The building casts a 66-foot shadow. You cast a 3-foot shadow. If you are 5 feet 6 inchestall, how tall is the building?

12. MODELS Truss bridges use triangles in their support beams. Molly made a model of atruss bridge in the scale of 1 inch 5 8 feet. If the height of the triangles on the model is4.5 inches, what is the height of the triangles on the actual bridge?

11}2

5}2

D F

E

e

f d

A C

B

b

c a

808

478478

568

E H

F

GD

C

318 598R Q S T

UP

Practice

Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

11-611-6


Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

11-611-6


Less

on

11-6Pre-Activity How are similar triangles related to photography?


How would you describe the shapes and sizes of the figures in the diagram?

Reading the Lesson

Complete each sentence.

1. In similar triangles, the angles of the two triangles can be matched so that

angles have equal .

2. If the angles of one triangle do not have the same measures as the angles of a second

triangle, then the two angles are not .

3. If two triangles have the same size and shape, then the measures of the corresponding

sides are .

Determine whether each pair of triangles is similar. Explain how you know that

your answer is correct.

4.

5.

6.


7. How can you use the idea that the corresponding sides of similar triangles areproportional to help you remember how to find the unknown lengths of the sides ofsimilar triangles?

358

358

208

1258

1258

208

4

3 3.5

8

67.5

328308

588

608

Skills Practice

Trigonometric Ratios

NAME ______________________________________________ DATE ____________ PERIOD _____

11-711-7


Less

on

11-7

For each triangle, find sin N, cos N, and tan N to the nearest ten thousandth.

1. 2. 3.

Use a calculator to find the value of each trigonometric ratio to the nearest

ten thousandth.

4. sin 20° 5. cos 32° 6. tan 75°

7. tan 17° 8. sin 38° 9. cos 55°

Use a calculator to find the measure of each angle to the nearest degree.

10. sin A 5 0.7624 11. cos L 5 0.8691 12. tan H 5 1.3024

13. tan V 5 0.5876 14. sin R 5 0.4320 15. cos S 5 0.3749

For each triangle, find the measure of the indicated angle to the nearest degree.

16. 17. 18.

Solve each right triangle. State the side lengths to the nearest tenth and the angle

measures to the nearest degree.

19. 20. 21. 21 m

28 m

A

CB

17 cm

548

A C

B

20 ft

288C A

B

412

?

5

?

113

8

?

8

15

17

N

P R

0.8 0.6

1FN

E

1026

24F

D

N


For each triangle, find sin T, cos T, and tan T to the nearest ten thousandth.

1. 2. 3.

Use a calculator to find the value of each trigonometric ratio to the nearest ten

thousandth.

4. sin 85° 5. cos 5° 6. tan 32.5°

Use a calculator to find the measure of each angle to the nearest degree.

7. sin D 5 0.5000 8. cos Q 5 0.1123 9. tan B 5 4.7465

For each triangle, find the measure of the indicated angle to the nearest degree.

10. 11. 12.

Solve each right triangle. State the side lengths to the nearest tenth and the angle

measures to the nearest degree.

13. 14. 15.

HIKING For Exercises 16 and 17, use the following information.

The 10-mile Lower West Rim trail in Mt. Zion National Park ascends 2640 feet.

16. What is the average angle of elevation of the hike from the canyon floor to the top of thecanyon? (Hint: Draw a diagram in which the length of the trail forms the hypotenuse ofa right triangle. Convert feet to miles.)

17. What is the horizontal distance covered on the hike?

18. RAMP DESIGN An engineer designed the entrance to a museum to include a wheelchairramp that is 15 feet long and forms a 6° angle with a sidewalk in front of the museum.How high does the ramp rise?

15 f30 ft

B C

A

13 cm648

A

C B

26 yd

518C B

A

1612

?40

42 ?13

9

?

16

88Ï·5

C

T

B25

724

R

P

T24

70

74T

X

Y

Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

11-711-7



NAME ______________________________________________ DATE ____________ PERIOD _____

11-711-7


Less

on

11-7

Pre-Activity How are trigonometric ratios used in surveying?


In which years were the measurements of the height of Mt. Everest inclosest agreement?

Reading the Lesson

1. Complete each sentence.

a. The legs of triangle MNR are segments and .

b. The hypotenuse of triangle MNR is .

c. The leg opposite /N is , and the leg adjacent to /N is .

d. The leg opposite /M is , and the leg adjacent to /M is .

2. Write K or S to complete each equation.

a. tan 5 b. sin 5

c. sin 5 d. cos 5

e. cos 5 f. tan 5

3. If you look straight in front of you and then up, the two lines of sight form an angle of

(depression/elevation). If you look straight in front of you and then

down, the two lines of sight form an angle of (depression/elevation).


4. What is one way you can remember the trigonometric ratios sine, cosine, and tangent?

ST}KT

KT}KS

ST}KS

ST}KS

KT}KS

KT}TS

K

S

T

M

N

R

Documents

Simplifying Radical Expressions...©Glencoe/McGraw-Hill 658 Glencoe Algebra 1 Solve each equation. Check your solution. 1. Ï2wb 5 8 2. 4Ï3w 5 Ïxw 3. 2Ï4wc 1 3 5 11 4. 6 2 Ï2wy