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 degA scientist measures the angle x and the distance y between the Earth and the shooting star. Which trig function would the scientist use to calculate the distance between the Earth and the Sun. (5 points)

Answer 1

The sketch of the question is given below:

The distance between the Earth and Sun in the image above is represented by b

To get b, we will use the relation below:

$\tan x^0=\frac{y}{b}$

To get b, we will cross multiply

$b=\frac{y}{\tan x^0}=y\times\frac{1}{\tan x^0}=y\times\cot x^0$

Hence,

b=y cotx°

Therefore, the trig function would the scientists use to calculate the distance between the Earth and the Sun is:

$y\cot x^0$