Setting Up Right Triangle Trig Ratios

We can find the length marked y using the tan function which is the ratio of ​ ​ (a)   . So we write tan (45) = ​ (b)   ​ . We can find x using the cos function and set up and solve the proportion ​​ (c)   45 = ​​ (d)   .

• opposite / adjacent

• y/5

• cos

• 5/x

• 90

• 5/y

• x/5

• y/x

• opposite / hypotenuse

• adjacent / opposite

A tourist views a deer from a height of 45 feet.  The horizontal distance between the tourist and the deer is 130 feet.  At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.  

• 19 degrees

• 45 degrees

• 71 degrees

• 138 degrees 

Since d is the side opposite the angle marked 39 degrees and 30 m is the ​ (a)   of the right triangle, we can use the sin function to find the distance marked d by setting up and solving the proportion sin(​ (b)   )=​ (c)   . When we solve for d, we get ​ (d)   .

• hypotenuse

• 39

• d/30

• 18.9

• 30/d

• 27.5

• cos

• tan

Find the trig value of sin A. [Note: A refers to the angle with vertex A.]

• A

• B

• C

• D

Find the trig value of sin C. [Note: C refers to the angle with vertex C.]

• A

• B

• C

• D

Use the diagram to match each expression with the correct value.

• 300/400

• 90 - x

• 500

• tan (90 - x)

• 400/300

• the distance from A to the plane

• The measure of the third angle of the triangle

• tan x

In the diagram on the left, one angle is marked "?". Use this to match each term with the correct value.

• 23

• the hypotenuse of the triangle

• 90 - ?

• the side that is opposite angle ?

• 23/28

• sin (?)

• 23/28

• cos (90 - ?)

• 28

• the measure of the third angle

Label each part of the triangle.

a

b

c

side adjacent to 30 degree angle

Hypotenuse

side opposite to 30 degree angle

Label the parts of the triangle.

a

b

c

side adjacent to 44 degree angle

Hypotenuse

side opposite the 44 degree angle

What is the length of u and v in this 30-60-90 triangle?

• u = 8 v = 4√3

• u = 4√2 v = 8

• u = 16 v = 8

• u = 4√3 v = 8