Question

A fire truck parks 16 feet away from a building. The fire truck extends its ladder 30 feet to the very top of the building. How tall is the building?

Answer 1

The height of the building is 25.38 feet

Step-by-step explanation:

Let AB denotes the height of the building.

Let BC denotes the distance between the fire truck and the building.

Let AC denotes the length of the ladder.

Using the Pythagorean theorem, we have,

`AC^2=AB^2+BC^2`

where AC = 30, BC = 16

Substituting the values, we have,

`30^2=AB^2+16^2`

Simplifying the terms, we get,

`900=AB^2+256`

Subtracting both sides by 256, we get,

`644=AB^2`

Taking square root on both sides of the equation, we get,

`√(644)=AB`

`25.38=AB`

Thus, the height of the building is 25.38 feet