Trigonometry Review

In this figure, triangle GHJ is similar to triangle PQR.

• A

• B

• C

• D

The figure below shows △ABC which is a right triangle.

Which of the listed values are equal to the sine of C?  Select All that apply. 

• A

• B

• D

• F

• G

In the three right triangles shown below, m∠C=m∠F=m∠I=40°. 

Complete the statement below about the triangles by selecting the correct ratio.

Because each statement contains a right triangle and a

40° angle, the triangles are 

similar by AA similarity, therefore, AB/AC=DE/DF = ______________.

• A

• B

• C

• D

Which of the equations show a correct trigonometric ratio for angle A in the right triangle below? Select all that apply.

• A

• B

• C

• D

• E

Andy is standing near a tree.  This diagram shows their shadow lengths.

What is the height, h, of the tree?

• A. 9 feet

• B. 13 feet

• C. 17 feet

• 1. D. 25 feet

At the end of her work day at the Ferguson Corporation, Sarah usually walks to the subway station to travel home. Today, she is walking to the Springdale Town Center first to take care of some errands. She will then continue walking to the subway station to travel home. The map of these routes is shown .

If Sarah walks to the Springdale Town Center from the Ferguson Corporation and then to the Subway Station, how much farther will she walk than if she walks directly to the Subway Station from the Ferguson Corporation? Show all of your work. 

• A. 1019.1 feet

• B. 2244.7 feet  

• C. 3263.8 feet

• D. 1263.8 feet 

Campsite A and campsite B are located directly opposite each other on the shores of Lake Omega, as shown in the diagram below. The two campsites form a right triangle with Sam's position, S. The approximate distance from campsite B to Sam's position is 1,300 yards.

• 1. A. The distance from Sam to campsite A is about 1,697 yds. The distance from Campsite A to B is about 1,090 yds.

• 1. B. The distance from Sam to campsite A is about 1,749 yds. The distance from Campsite A to B is about 2,140 yds

• 1. C. The distance from Sam to campsite A is about 1,697 yds. The distance from Campsite A to B is about 1,096yds.

• 1. D. The distance from Sam to campsite A is about 2244 yds. The distance from Campsite A to
     B is about 2,141 yds.

In triangle ABC, angle A measures 30 degrees and angle B measures 60 degrees. If side AC measures 8 units, what is the length of side BC?

• A)  4.6​ units

• B)  4 units
  

• C)  8 units
  

• D)  16 units

In the diagram below of right triangle ABC, altitude BD is drawn to hypotenuse AC.

If BD = 4, AD = 2, and CD = x, what is the length of CD?

• 1. A. 5 

• B.  2 

• C. 8 

• D. 11

A sketch of a right triangle roof frame named ABC. The bottom side AC measures 10 meters and stretches across the house. The homeowner wants the height of the truss, which goes from the base to the highest point, to be no more than 3 meters so they can see the sunset.

If the horizontal distance from A to the highest point of the truss, represented in this figure by 

AD, is 2 meters, will this triangular truss satisfy the requirement of the homeowner? What is BD that satisfies the given?

• A. Yes ; BD = 3

• B. No, BD =4

• C. No, BD= 5

• D. Cannot be Determined