Question

a safety regulation states that the maximum angle of elevation for a rescue ladder is 72°. a fire departments longest ladder is 110 feet. what is the maximum safe rescue height, a? round your answer to the nearest whole number.

Explanation:

Step1: Use the sine function

In the right - triangle, the sine of an angle is defined as $\sin A=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $A = 72^{\circ}$, the hypotenuse $c = 110$ ft, and the opposite side is the height $a$. So, $\sin72^{\circ}=\frac{a}{110}$.

Step2: Solve for $a$

Multiply both sides of the equation by 110: $a = 110\times\sin72^{\circ}$.
We know that $\sin72^{\circ}\approx0.9511$. Then $a=110\times0.9511 = 104.621$.

Answer:

$105$ ft