Question

Help me fill this out thanks

Answer 1

10

Explanation:

We cannot use the Pythagorean Theorem here because we only have one side length. However, we can use the fact that
`(a)/(sin(A)) =(b)/(sin(B))=(c)/(sin(C))`

I decided to make the corner with the 60° as ∠A, the corner with the 30° as ∠B, and the corner with the right angle as ∠C. While then making side a as the unmarked side, side b as the side with 5, and the hypotenuse p as side c.

Since we do not need to solve for a in this equation to solve for p, we can simply use the sides and numbers we are given.

Manipulating two of our equations, preferably the equations with the variables b and c, we can get
`(b)/(sin(B))=(c)/(sin(C))` and solving for c, which is p in this case, will give us
`c=(bsin(C))/(sin(B))`

Plugging in the numbers we have gives us
`c=(5sin(90))/(sin(30))` = 10 mi