Question

A blimp is flying directly above a football field. The angle of depression to the base of one goal post is 40o. The angle of depression to the base of the other goal post is 72o. If the goal posts are 360 feet apart, how high is the blimp flying

Answer 1

237.65 feet

Explanation:

From the diagram attached,

Let the height of the blimp above the ground be h

From triangle A of the diagram,

tan18° = (360-y)/h

h = (360-y)/tan18°..................... Equation 1

Also

From triangle B in the diagram,

tan50° = y/h

h = y/tan50°.............................. Equation 2

Equation equation 1 and equation 2

(360-y)/tan18° = y/tan50°

tan50°(360-y) = tan18°(y)

1.19(360-y) = 0.325(y)

428.4-1.19y = 0.325y

428.4 = 0.325y+1.19y

1.515y = 428.4

y = 428.4/1.515

y = 282.8

Substituting the value of y into equation 2

h = 282.8/tan50°

h = 282.8/1.19

h = 237.65 feet.