a safety regulation states that the max. angle of elevation for a rescue ladder is 72 degrees. if a fire department's longest ladder is 115ft, what is the max. safe rescue height? (nearest foot)

Answer 1

We are given the maximum length of the ladder which would lay against the wall so this is our hypotenuse

We are given the increasing height maximum of 72 degrees which would be our bottom right triangle angle

We should use sine to calculate the height or side "X" of the highest safest spot the ladder can reach

Sin(72) = x/115ft

115ft*sin(72) = x

x= 29.189 ft = 29 ft

Answer 2

a safety regulation states that the max. angle of elevation for a rescue ladder is 72 degrees. if a fire department's longest ladder is 115ft, what is the max. safe rescue height? (nearest foot)

The ladder's length is the hypotenuse of a right triangle with the angle of elevation, call it ∅≤72°. We know that sin∅=H/R where H is the height of the triangle and R=115 ft.

H≤Rsin∅

H≤115sin72°=109 ft

H≤109 ft