To measure the height of the cloud cover at an airport, a worker shines a powerful spotlight upward at an angle 85deg from the horizon.

Question

Question: To measure the height of the cloud cover at an airport, a worker shines a powerful spotlight upward at an angle 85deg from the horizon. An observer 500m away measures the angle of elevation to the spot of light to be 40deg. Find the height h of the cloud cover (to the nearest meter)

Comment: I've made a triangle, split it in half and labeled it h, for height. On the right triangle to the left, I put 40 deg, and the right triangle on the right, I put 85 deg. The base I put as 500M. I know that Tangent is opposite over adjacent, so I put tan(40deg)=h/x, but this gave me a weird decimal of x which equals h. Can someone please help?

Answer 1

Try this and let us know how it goes after these hints.

At the point where the height (h) meets the base (500) separate the base into x and 500-x. Then tan 40 = h/x and tan 85 = h/(500-x). Now you have two equations with two unknowns. Try using the substitution method (solve one equation for x (or h) and substitute into the other equation,