Question

Need help with this review. To explain more and help with the real test I have later on this week.

Answer 1

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. Given an angle of the right triangle, the ratio between the opposite side and the adjacent side to this angle is equal to the tangent of this angle. Using this relation in our problem, we have

`\tan \theta=(1)/(d)`

If we take the inverse on both sides, we have

`\begin{gathered} (\tan \theta)^(-1)=((1)/(d))^(-1) \\ \cot \theta=d \end{gathered}`

Now, using a calculator to find the cotangent of theta, we have

`d=\cot \theta=4130914.16821`

And this is the distance between the sun and the star.