Trigonometry Story Problem

Question

To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle of 73° from the horizontal. An observer 734 m away measures the angle of elevation to the spot of light to be 48°. Find the height of the cloud cover.

Answer 1

Draw a perpendicular from the cloud to the ground. Label intersection G

Labe first observation point A, second observation point B, height of the cloud h

AG = x

BG = 734 - x

tan 48° = h / BG

tan 73º = h / AG

Substitute values and solve for h.

Answer 2

734 distance

73 angle and 2nd angle = 48

sounds like an ASA triangle 73- 734- 48 triangle

3rd angle = 180- 73- 48 = 180- 121 = 59 degrees

use the Law of Sines to find other two sides

or use a triangle calculator on line

608.556 meters is the height

find the area, divide by the base to get the height

find the area with heron's formula

with luck no mistakes. Use a calculator

even better use a triangle online calculator

try a couple if they give the same answer

odds are good it's right