Question

When flying a kite Peter without 45 feet of string and anchors it to the ground. He determines the angle of elevation of the kite is 63°. What is the height of the kite from the ground? Round to the nearest 10th.

Answer 1

We're going to  use trigometric functions! 

So we know the angle is 63° (Ф=63°)
the length of the string is 45 ft (hyp=45)
and we need to solve for height (h=?)

Using sinФ=$\frac{opposite}{hypotenuse}$

We can rewrite it as
sinФ=$\frac{height}{hypotenuse}$

By isolating the height (h) we can find the value
sinФ=$\frac{height}{hypotenuse}$
h= hyp(sinФ)

Then insert value of hyp, Ф and find height
h= hyp(sinФ) = 45sin63 = 40 ft

The kite is 40 ft off the ground