Question

((Please Answer with A B C or D))
A firefighter needs to rescue a person from a burning building. The person is located 50 feet up in the building. If the base of the ladder is on top of a 10 foot tall fire truck and the ladder is 105 feet long, what is the approximate angle of elevation for the rescue ladder?
A. 68°
B. 69°
C. 21°
D. 22°

Answer 1

Hello!

The answer is:

The correct option is:

$D.22\°$

Why?

We can calculate the angle of elevation of the rescue ladder (formed triangle) using the following trigonometric formula:

$Sin(\alpha)=\frac{y}{hypothenuse}$

Where,

y, is represented by the height where the person is located (50 feet) less the height of the top of the fire truck (10 feet)

hypothenuse, is represented by the length of the ladder (105 feet)

So, substituting and calculating we have:

$Sin(\alpha)=\frac{y}{Hypothenuse}\\\\\alpha =Sin(\frac{Height}{LadderLength})^{-1}\\\\\alpha =Sin(\frac{50feet-10feet}{105feet})^{-1}=Sin(\frac{40feet}{105feet})^{-1}\\\\\alpha=Sin(\frac{40feet}{105feet})^{-1}=Sin(0.38)^{-1}=22.33\°=22\°$

Hence, we have that the correct option is:

$D.22\°$

Have a nice day!