Today – Monday, March 4, 2013

Warm Up: Which method to use to solve missing angles or sides of a right triangle

Review: Using inverse trig to find missing angles

Learning Target : Review solving for missing sides of right triangles using special triangles and trigonometry

QUIZ: Trigonometry and special right triangles

Independent Practice

30 °2𝑦

WARM UP: Decide which method would you use to find the missing sides of the right triangle (Pythagorean Theorem, Special Right Triangles, or Trig), then find the missing sides.

𝑥

621° 𝑦𝑥 9

7𝑥

METHOD TO FIND TRIG ANGLES:

𝑜𝑝𝑝𝑜

𝑠𝑖𝑡𝑒 h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

“”

θ=𝑡𝑎𝑛− 1(𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 )

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

1. Find the opposite, adjacent and hypotenuse of your right triangle.

θ=𝑐𝑜𝑠− 1( 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 )

θ=𝑠𝑖𝑛− 1( 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 )

2. Use the trig function that contains the sides of your triangle.3. Use the inverse trig function to calculate the angle.

912

PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.

𝑥

Use cosine ratio

Substitute known values

Use inverse cosine

Solve for x using calculator

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

8

14

PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.

𝑥

Use tangent ratio

Substitute known values Use inverse tangent

Solve for x using calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

13

57

PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.

𝑥

Use sine ratio

Substitute known values

Use inverse sine

Solve for x using calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

Solve for x using 8

6

PRACTICE: Find angle x using inverse trigonometric functions. Round your answer to the nearest hundredth.

𝑥 h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒10

Solve for y using

𝑦

There are multiple ways to solve this problem, you may

choose any trig function because all sides are given!

Inverse Trig Practice

15 minutes

We will check answers as a class.

Basic Right Triangle Problems:FINDING MISSING SIDES USE:• Pythagorean Theorem• Special Right Triangles:

30-60-9045-45-90

• Trig Ratios: sinx, cosx, tanx

FINDING MISSING ANGLES USE:• Inverse Trig:

:

√𝟐𝒙𝒙 45 °

45 °𝒙

𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆=𝒍𝒆𝒈 ·√𝟐In a triangle:

𝟐 𝒙𝒙

60 °

30 °

√𝟑 𝒙

In a triangle:

METHOD TO FIND MISSING SIDES USING SPECIAL TRIANGLES:

h𝑠𝑜𝑟𝑡

𝑙𝑒𝑔

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑙𝑜𝑛𝑔𝑙𝑒𝑔30 °

1. Determine which special triangle right triangle is shown-one angle will always be given. 2. Determine whether sides of the triangle that is given, is a leg (short or long or equal) or a hypotenuse. 3. Use given information from special triangle to plug into given equations, then solve for missing side.

𝒉𝒚𝒑

𝒆𝒒𝒖𝒂

𝒍𝒍𝒆𝒈

45 °

𝒆𝒒𝒖𝒂𝒍 𝒍𝒆𝒈

𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆=𝒍𝒆𝒈 ·√𝟐

𝑥 9√2

PRACTICE: Find the value of x. Write your answer in the simplest radical form.

𝑥

Substitute known values Divide by

Simplify

20

𝑥

PRACTICE: Find the value of x and y. Write your answer in simplest radical form.

30 °

60 °

𝑦

Substitute known values Divide Simplify

Substitute known values

Simplify

√3 𝑥

PRACTICE: Find the value of x and y. Write your answer in simplest radical form.

30 °

60 °

𝑦 Substitute known values

Multiply

Substitute known values

Multiply Simplify

¿2√3

¿3

3√2 𝑥

PRACTICE: Find the value of x. Write your answer in the simplest radical form.

3√2

Substitute known values Multiply square roots

Simplify

TRIGONOMETRIC RATIOS:

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

“”𝑆𝐼𝑁𝐸 : 𝑠𝑖𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝑂𝐻

𝐶𝑂𝑆𝐼𝑁𝐸 :𝑐𝑜𝑠 𝜃=𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝐴𝐻

𝑇𝐴𝑁𝐺𝐸𝑁𝑇 :𝑡𝑎𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

=𝑂𝐴

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

METHOD TO FIND MISSING SIDES USING TRIGONOMETRY:

𝑜𝑝𝑝𝑜

𝑠𝑖𝑡𝑒 h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

“”

1. Find the opposite, adjacent and hypotenuse of your right triangle. 2. Use the trig function that contains the sides of your triangle to set up your equation.3. Solve for x, then use your calculator to evaluate for the missing side.

𝑥

52

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

26 °

Use tangent ratio Substitute known values Multiply by x on both sides

Divide by , both sides Solve for x using a calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

67 𝑥

PRACTICE: Find x using the tangent ratio. Round answer to the nearest tenth.

46 °

Use sine ratio

Substitute known values

Multiply by 67 on both sides

Solve for n using calculator

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

40

𝑥

PRACTICE: Find x using the cosine ratio. Round answer to the nearest tenth.

65 °

Use cosine ratio Substitute known values Multiply by x on both sides

Divide by , both sides Solve for x using a calculator

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

Solve for x using 𝑥

6

PRACTICE: Find x and y using the tangent ratio. Round answer to the nearest tenth.

52 ° h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒

𝑦𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒

Solve for y using

HOMEWORK:

If finished, work on other assignments:

HW #1: Pg. 436: 3-29 oddHW #2: Pg. 444: 1-6, 8, 10, 12HW #3: Pg. 461: 3-18HW #4: 7.4 Special Triangles WS (Kuta)HW #5: Pg. 470: 18-20, 24-29, 31, 32

Pg. 477: 10-15, 18-27HW #6: Pg. 485: 3-8, 10-18