7.57.5 Apply the Tangent RatioBell Thinger

Find the values of the variables.

1.

ANSWER x = 2 6, y = 2 15

2.

ANSWER 15 2

7.5

7.5 Example 1

Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places.

SOLUTION

tan S =opp S

adj. to S= RT

ST= 80

18= 40

9 4.4444

tan R =opp R

adj. to R= ST

RT= 18

80= 9

400.2250=

7.5 Guided Practice

Find tan J and tan K. Round to four decimal places.

ANSWER 0.7500, 1.3333

ANSWER 0.5333, 1.8750

7.5 Example 2

ALGEBRA Find the value of x.

SOLUTION

Use the tangent of an acute angle to find a leg length.

tan 32° =opp. adj.

Write ratio for tangent of 32°.

tan 32° 11

=x

Substitute.

x tan 32° = 11 Multiply each side by x.

x = 11 tan 32°

Divide each side by tan 32°.

x 11 0.6249

Use a calculator to find tan 32°.

x 17.6 Simplify.

7.5 Example 3

LAMPPOST Find the height h of the lamppost to the nearest inch.

tan 70° =opp. adj.

Write ratio for tangent of 70°.

tan 70° h

=40

Substitute.

40 tan 70° = h Multiply each side by 40.

109.9 h Use a calculator to simplify.

The lamppost is about 110 inches tall.

7.5 Example 4

Use a special right triangle to find the tangent of a 60° angle.

STEP 1 Because all 30° - 60° - 90° triangles are similar, you can simplify your calculations by choosing 1 as the length of the shorter leg. Use the 30° - 60° - 90° Triangle Theorem to find the length of the longer leg.

longer leg = shorter leg 3 30o- 60o- 90o Triangle Theorem

x = 1

3 Substitute.

x = 3 Simplify.

7.5 Example 4

STEP 2

tan 60° =opp. adj.

Write ratio for tangent of 60o.

tan 60° =3

1Substitute.

tan 60° = 3 Simplify.

The tangent of any 60° angle is 3 1.7321

Find tan 60°.

7.5 Guided Practice

Find the value of x. Round to the nearest tenth.

ANSWER 12.2

ANSWER 19.3

3.

4.

7.5Exit Slip

Use this diagram for Exercises 1- 4.

1. If a = 18, b = 80 and c = 81, find tan B and tan A. Write each answer as a fraction and a decimal rounded to 4 places.

ANSWER tan B = 9

40 = 4.4444; tan A = = 0.2250940

7.5

Use this diagram for Exercises 1- 4.

2. If a = 17 and m A = 31° , find b to the nearest tenth.

ANSWER 28.3

Exit Slip

7.5

Use this diagram for Exercises 1- 4.

3. If a = 9 and m B = 74° , find b to the nearest tenth.

ANSWER 31.4

Exit Slip

7.5

Use this diagram for Exercises 1- 4.

ANSWER 64.3

4. If a = 5 and m B = 11° , find the number of square units in the area of ABC to the nearest tenth.

Exit Slip

7.5

5. Find x, y and z.

ANSWER 3 2x = 6 2z = 3 6y = , ,

Exit Slip

7.5

Find the value of the variable.

6.

ANSWER 3 5

Exit Slip

7.5

HomeworkPg 487-490#19, 21, 25, 28, 31