Shooting Star Math

Question

A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x deg

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the shooting star.

Answer 1

I can't see the figure but I'm guessing the right angle is the angle where Earth is the vertex. Let s be the distance between Earth and the shooting star. The distance from the Earth to the Sun is 93 million miles; Using trig, we have:

tan x = s/93

93 tan x = s

The units are missions of miles. In words, "The ratio of the Earth-Shooting Star distance to the Earth-Sun distance is equal to the tangent of angle x. Since x and the Earth-Sun distance are known, use the tangent function to find s."

If you can, attach the figure to the problem to be sure my guess about the triangle was correct.