Question

A shooting star forms a right triangle with the Earth and the Sun, as shown below:

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

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

Here is my answer: First, he uses tangent to find the distance between Earth and Shooting star (tan x=opposite/y). Then, he solves by simplifying and by plugging in the numbers for x degrees and side y, which only he knows.

y tan x=opposite

This will give him the answer.

Answer 2

What I want to know is is this the final answer, or is there another step? I believe that this only gives him the third angle, not the third side.

Answer 3

Er, opposite side not third side.

Answer 4

So, as you said

\[\tan = \frac{ opposite }{ adjacent }\]

He found the angle, and he found the adjacent and needs the opposite

\[\tan(x) = \frac{ opposite }{ y }\]
Multiplying by y gives you

\[(y)(\tan(x)) = opposite\]

So I see no fault in your answer

Answer 5

Thanks for confirming, last question and im done with the class so just trying to make sure.

Answer 6

Anytime