Solving Right Triangles with Pythagorean Theorem and Trig Ratios

Using the Pythagorean Theorem and Trig Ratios to Solve Right Triangles

Special Right Triangles

30-60-90 Triangle

• Side length are always in these proportions

• We will use this when we are deriving the Unit Circle

Multiple Choice

• a=√6   b=√2
• a=4   b=2
• a=√6   b=2
• a=2   b4

Multiple Choice

What are x and y in this 30-60-90 triangle?

• x = 6 y = 3√3
• x = 1.5√3 y =1.5
• x = 3√3 y = 6
• x = √3 y = 2√3

Multiple Choice

What is the measure of side c?

• 6
• 6√2
• 6√3
• 12

45-45-90 Triangle

• Side length are always in these proportions

• Congruent angles have congruent sides across from them

• We will use this when deriving the Unit Circle.

Multiple Choice

Determine the value of c.

• c = 6√3

• c = 12√3

• c = 18

• c = 18√2

Multiple Choice

Use the 45-45-90 theorem to solve for the hypotenuse.

• 16

• 8

• 8√2

• √16

Multiple Choice

What is the measure of side c?

• 7

• $$\frac{7}{\sqrt{2}}$$

• 7√2

• 14

Trig - Find Side Lengths and Angle Measures

By Andrew Schmitt

Use the image to the right to indicate how trig functions should be set up to solve for a missing side or angle.

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Setting up Trig Equations ​

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Multiple Choice

What equation can be used to solve for x?

• Sin(40°)= x/40 
• Sin(40º)=x/19
• Cos(40º)=x/19
• Tan(40°)=19/x

Multiple Choice

Choose the correct ratio.

• cos(33)=x/14
• sin(33)=x/14
• cos(33)=14/x
• sin(33)=14/x

After you have the equation set up, decide on how to solve it!

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If x is on TOP, multiply!

If x is on BOTTON, divide!​

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​After setting it up, solve!

Multiple Choice

Using the equation already set up, solve for x. Round to the nearest tenth.

• 103.5
• 4.7
• 55.0
• 23.4

Multiple Choice

Using the equation already set up, solve for x. Round to the nearest tenth.

• 9.8
• 0.1
• 0.038
• 9.9

Multiple Choice

Find x round to the nearest tenth.

• 46.1
• 4.9
• 73.5
• 68.6

Multiple Choice

Find the measurement of the missing side indicated

• 4.39
• 3.21
• 2.19
• 2.05

Inverse Trig Ratios

We use inverse trig functions to find angle measures.

(You will need a calculator)

Multiple Choice

Set up the problem...

• sin X = 41/28
• tan X = 41/28
• cos X = 28/41
• sin X = 28/41

Multiple Choice

Find each angle measure to the nearest degree.

• 22
• 21
• 20
• 19

Multiple Choice

Find each angle measure to the nearest degree.

• 64
• 67
• 62
• 60

Multiple Choice

Find each angle measure to the nearest degree.

• 83
• 89
• 80
• 88

Multiple Choice

Solve for the missing angle.

• 50.5 degrees
• 12.7 degrees
• 36.9 degrees
• 72.2 degrees

Multiple Choice

Solve for m∠N                                                                                                                                               

• 14
• 65
• 76
• 53

Multiple Choice

Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle.

• 49.6°

• 57.4°

• 45.8°

• 54.5°