Question

A safety regulation states that the maximum angle of elevation for a rescue ladder is 72°. A fire department's longest ladder is 110 feet. What is the maximum safe rescue height?

Answer 1

104.6

Explanation:

Answer 2

The maximum safe rescue height is 104.6 feet above the height of the ground.

Explanation:

Consider a triangle ABC where C is the point where the rescue ladder is standing and AB be the building and Ladder making an angle of 72° as shown.

We have to find the height of the building.

Let x be the height of building

Using Trigonometric ratio,

`\sin C=\frac{\text{Perpendicular}}{\text{Hypotenuse}}`

`\sin 72^(\circ)=(AB)/(BC)`

`\sin 72^(\circ)=(x)/(110)`

`x=110 * \sin 72^(\circ)`

`x=104.6`

So, the maximum safe rescue height is 104.6 feet above the height of

the ground.