Question

A 25 foot ladder is leaning against a house. If the angle of Elevation of the ladder is 72 degrees:

How high up the house does the ladder touch?
How far away is the ladder from the house?
Round to the nearest tenth.

Answer 1

1. 23.8

2. 7.7

Explanation:

for the first blank

use sin because x is opposite and 25 is hypotenuse

set up an equation:

sin(72)= (x/25)

multiply both sides by 25:

25(sin(72))= (x/25)25

25(sin(72))= x

multiply 25 by sin(72):

23.8 = x

for the second blank

use cos because x is adjacent and 25 us hypotenuse

set up an equation:

cos(72)= (x/25)

multiply both sides by 25:

25(cos(72))= (x/25)25

25(cos(72))= x

multiply 25 by cos(72):

7.7= x