A firefighter extends a ladder against the side of a house. The ladder makes a 32°\degree° angle with the ground. The base of the ladder is 25 feet from the house. Find how high the ladder reaches up the side of the house to the nearest tenth of a foot. *Draw and label a picture, set up an equation, and solve*

29.5 feet

Step-by-step explanation:

A firefighter extends a ladder against the side of a house. The ladder makes a 32°\degree° angle with the ground. The base of the ladder is 25 feet from the house. Find how high the ladder reaches up the side of the house to the nearest tenth of a foot.

We solve using Trigonometric function of Cosine

= cos theta = Adjacent/Hypotenuse

Theta = 32°

Adjacent = 25 feet

Hypotenuse = Height of the ladder

= cos 32 = 25/x

x = 25/cos 32

x = 29.479460084 feet

Approximately= 29.5 feet

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value