Solving tri. with trig. functions

Trig - Find Side Lengths and Angle Measures

By Andrew Schmitt

Solving Right Triangles

Pythagorean Theorem​

• When a problem involves only sides, use Pythagorean Theorem

Trigonometry

• When a problem involves both sides and angles, use SOH-CAH-TOA

Trigonometric Ratios

Remember, each of these ratios relies on you identifying the sides of the triangle based on your reference angle.

Multiple Choice

Which equation should be used to find the missing side length?

• $$\cos\left(33\right)=\frac{x}{14}$$  

• $$\sin\ \left(33\right)=\frac{x}{14}$$  

• $$\tan\ \left(33\right)=\frac{x}{14}$$  

• $$\tan\left(33\right)=\frac{14}{x}$$  

• $$\cos\left(33\right)=\frac{14}{x}$$  

Multiple Choice

If you are trying to find the hypotenuse, then which equation should be used to find the missing side length?

• $$\tan\left(35\right)=\frac{x}{12}$$   

• $$\tan\left(35\right)=\frac{12}{x}$$  

• $$\sin\left(35\right)=\frac{12}{x}$$  

• $$\cos\left(35\right)=\frac{12}{x}$$  

• $$\cos\left(35\right)=\frac{x}{12}$$  

Multiple Choice

Find the length of x.

• 4.98
• 5.98
• 3.20
• 4.18
• 7.13

Multiple Choice

Find the length of x.

• 4.39
• 3.21
• 2.19
• 2.05
• 1.71

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4
• 55.2
• 20.15
• 19.4
• 37.6

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest degree.

• 32°
• 44°
• 61°
• 50°
• 46°

Multiple Choice

Solve for the missing angle.

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

Multiple Choice

Solve for x. Round to the nearest tenth.

• 9.8
• 0.1
• 0.038
• 9.9

Multiple Choice

Solve for x.

• 24.20
• 4.92
• 290.4
• 29.75

Multiple Choice

Solve for the misssing distance

• 18.9
• 19.5
• 47
• 27.5

Multiple Choice

Find the measure of the missing angle.

• 64^o
• 26^o
• 61^o
• .008^o

Multiple Choice

Use inverse trig ratios to solve for the missing angle

• 32°
• 44°
• 61°
• 50°