Question

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

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

Answer 1

The scientist can use only the angle x and the distance y to calculate the distance between the Earth and the Sun using the cosine function.

The cosine of an angle is equal to the ratio of the length of the adjacent side and the length of the hypotenuse. In equation form:

cos x = BC / y

Solving for BC

BC = y cos x

BC is the distance between the Earth and the Sun

Answer 2

Let the distance between the earth and the sun be z, then
tan x = y/z
z = y tan x

Therefore, the distance between the earth and the sun can be obtained by multiplying t to the tangent of x.