Ch.9 Review: Right Triangles & Trigonometry

Last updated almost 2 years ago

16 questions

Pythagorean Theorem

Special Right Triangles

9.3 Similar Right Triangles

Tangent Ratio

Sine & Cosine Ratios

Ch.9 Review: Right Triangles & Trigonometry

Last updated almost 2 years ago

16 questions

Pythagorean Theorem

Find the value of x for each triangle.

1. x = _______ 

2. x = _______

Tell whether the triangle is a right triangle.

Special Right Triangles

Find the values of x and y. Write your answer in simplest form.

14. x = _______     y = _______ 

16. x = _______

Find x.

9.3 Similar Right Triangles

Identify the similar right triangles. Then find the value of x.

19. x = _______ 

20. x = _______

Tangent Ratio

Find the tangents of the acute angles in the right triangle.  
You just need to find the RATIO.
Write each answer as a fraction or as a decimal.


Angle J = _______ 
Angle L = _______ 

Find the value of x.

30. x = _______ 

31. x = _______

The angle of elevation from the bottom of a fence to the top  of a tree that is 4 feet from the fence is 75°. Round answers to the nearest tenth.

a. How tall is the tree? _______ 

b. The angle of elevation from the bottom of the fence to the ﬁrst limb on the the tree is 62°. How high is the limb? _______ 

Sine & Cosine Ratios

Find sin X, sin Z, cos X, and cos Z. Write each answer as a fraction.
sin X = _______ 
sin Z = _______ 
cos X = _______ 
cos Z = _______ 

Write sin 72° in terms of cosine. 
_______ 

Write cos 29° in terms of sine. 
_______ 

Find the value of s and t using sine and cosine. Round answers to nearest hundredth.


r =  _______ 
s = _______ 

The Niagara Falls Incline Railway has an angle of elevation of 30° and a total length of 196 feet. How many feet does the Niagara Falls Incline Railway rise vertically?

Solve the right triangle. Round to nearest tenth.

Angle X = _______ 

Angle Z = _______ 

XY = _______

A doctor is using a treadmill to assess the strength of a patient's heart. He sets the 48 inch long treadmill at an incline of 10 degrees, how high is the end of the treadmill raised?

A person in a hot air balloon is looking down with an angle of depression of 36 degrees at their car 75 feet away (straight line distance).
How high is the balloon?

A student wants to know how tall the flagpole at her school is, her eye level is 5.5 feet above the ground and she stands 36 feet from the base of flagpole.

If the angle of elevation is 25 degrees, what is the height of the flagpole?

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Ch.9 Review: Right Triangles & Trigonometry

Ch.9 Review: Right Triangles & Trigonometry

Tell whether the triangle is a right triangle.

Find x.

The Niagara Falls Incline Railway has an angle of elevation of 30° and a total length of 196 feet. How many feet does the Niagara Falls Incline Railway rise vertically?

A doctor is using a treadmill to assess the strength of a patient's heart. He sets the 48 inch long treadmill at an incline of 10 degrees, how high is the end of the treadmill raised?

A person in a hot air balloon is looking down with an angle of depression of 36 degrees at their car 75 feet away (straight line distance).How high is the balloon?

A student wants to know how tall the flagpole at her school is, her eye level is 5.5 feet above the ground and she stands 36 feet from the base of flagpole.If the angle of elevation is 25 degrees, what is the height of the flagpole?

Tell whether the triangle is a right triangle.

Find x.

The Niagara Falls Incline Railway has an angle of elevation of 30° and a total length of 196 feet. How many feet does the Niagara Falls Incline Railway rise vertically?

A doctor is using a treadmill to assess the strength of a patient's heart. He sets the 48 inch long treadmill at an incline of 10 degrees, how high is the end of the treadmill raised?

A person in a hot air balloon is looking down with an angle of depression of 36 degrees at their car 75 feet away (straight line distance).How high is the balloon?

A student wants to know how tall the flagpole at her school is, her eye level is 5.5 feet above the ground and she stands 36 feet from the base of flagpole.If the angle of elevation is 25 degrees, what is the height of the flagpole?

A person in a hot air balloon is looking down with an angle of depression of 36 degrees at their car 75 feet away (straight line distance).
How high is the balloon?

A student wants to know how tall the flagpole at her school is, her eye level is 5.5 feet above the ground and she stands 36 feet from the base of flagpole.

If the angle of elevation is 25 degrees, what is the height of the flagpole?

A person in a hot air balloon is looking down with an angle of depression of 36 degrees at their car 75 feet away (straight line distance).
How high is the balloon?

A student wants to know how tall the flagpole at her school is, her eye level is 5.5 feet above the ground and she stands 36 feet from the base of flagpole.

If the angle of elevation is 25 degrees, what is the height of the flagpole?