TODAY IN GEOMETRY…

Review: Methods solving for missing sides of a right triangle

Learning Target: 7.6 Finding an angle using inverse Trigonometry

Independent Practice

Basic Trig Problems in 3 categories:

• Pythagorean Theorem• Special Right Triangles:

30-60-9045-45-90

• Trig Ratios: Sin, Cos, Tan

𝑥6

PRACTICE: Identify what category this problem lies in (Pythagorean, Special Right Triangles, or Trig Ratios). Solve for the missing variables.

30 °𝑦

Substitute known values

Multiply Divide

Substitute known values

Simplify

Special Right Triangle

𝑎

17.821.2

PRACTICE: Identify what category this problem lies in (Pythagorean, Special Right Triangles, or Trig Ratios). Solve for the missing variable.

The unknown side is attached to the right angle so it is a leg of the triangle.

Use the Pythagorean theorem to find the missing leg:

Given two sides:Pythagorean Theorem

19𝑥

PRACTICE: Identify what category this problem lies in (Pythagorean, Special Right Triangles, or Trig Ratios). Solve for the missing variable.

48 ° Use sine ratio

Substitute known values Multiply by x on both sides

Divide by , both sides Solve for x using a calculator

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒Given one side and an angle:

Trig Ratios

30 °4

𝑦

Which method would you use to find the missing sides of the right triangle (Pythagorean Theorem, Special Right Triangles, or Trig)?

𝑥

652 ° 𝑦 𝑥8

7

Find Trigonometric angles using inverse

𝜃𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

TRIGONOMETRIC RATIOS:

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡𝜃

“”𝑆𝐼𝑁𝐸 : 𝑠𝑖𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝑂𝐻

𝐶𝑂𝑆𝐼𝑁𝐸 :𝑐𝑜𝑠 𝜃=𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

=𝐴𝐻

𝑇𝐴𝑁𝐺𝐸𝑁𝑇 :𝑡𝑎𝑛𝜃=𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

=𝑂𝐴

𝑺𝑶𝑯𝑪𝑨𝑯𝑻𝑶𝑨

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.

13

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

2436

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

43

92

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!

HOMEWORK #7:

Pg. 485: 3-8, 10-18

If finished, work on other assignments:

HW #1: Pg. 436: 3-29 oddHW #2: Pg. 444; 1-6, 8, 10, 12HW #3: Pg. 461: 3-18IN CLASS WORK #4: 7.4 Special Right Triangles WSHW #5: 7.5 WS-x on topHW #6: 7.5 WS-x on bottom