Question

2. You are standing 15 feet from a tree. You want to get an apple from the tree using a ladder that is 25 feet long. What is the height of the tree? What is the angle of elevation?

Answer 1

h = 20 ft

theta =53.13010235

Explanation:

First we can find the height by the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs

15^2 + h^2 = 25^2

225 + h^2 = 625

h^2 = 625 - 225

h^2 = 400

Taking the square root of each side

h = 20 ft

Now using trig functions

cos theta = adj side / hyp

cos theta = 15/25

Taking the inverse cos of each side

cos^-1 ( cos theta) = cos^-1 ( 15/25)

theta =53.13010235