Section 5-4

Applying Trig Functions

Objective: Students will be able to use trigonometry to find the measures of the sides of right triangles.

Example 1:

If B = 42° and a = 12, find c, b, and A.

You know the measure of the side adjacent the angle.

The cosine function relates the side adjacent to the angle and the hypotenuse.

cos𝜃=𝑠𝑖𝑑𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

cos 42 °=12𝑐𝑐 cos 42°=12𝑐=

12cos 42 °

C = 16.1476

C

tan𝜃=𝑠𝑖𝑑𝑒𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

tan 42 °= 𝑏12

12 tan 42°=𝑏10.8048=𝑏𝑏≈10.8

A + B + C = 180

A + 42 + 90 = 180

A = 48

Example 2:RECREATION A child holding on to the string of a kite gets tired and decides to put the

string on the ground and secure it with a brick. The length of the string from the brick to the kite is 240 feet.

A) If the angle formed by the string and the ground is 50.275°, how high is

the kite?

We know the angle and the hypotenuse. We want to findthe height of the kite (h).

sin 𝜃=𝑠𝑖𝑑𝑒𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

sin 50.275= h240

240sin 50.275=h

h = 184.589The height of the kite is about 184.6 feet.

B) What is the horizontal distance between the kite and the brick?

Her we want to know the side adjacent the angle. So we will use the cosine function.

cos𝜃=𝑠𝑖𝑑𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

cos 50.275= 𝑑240

240 cos 50.275 = d

D = 153.3848

The horizontal distance between the brick and the kite is about 153.4 feet.