Question

A ladder 15 feet long leans against the top of a structure at a 60 degree angle to the ground. What is the height of the building to the nearest hundredth of a foot?

Answer 1

The height of the building is the long leg. 12.99 foot

Explanation:

The triangle is a 30° - 60° - 90°.

In this type of triangle the hypotenuse = the short leg × 2. (it is opposite the 30° angle). The Long leg = the short leg √3

hypotenuse is the length of the ladder.

`hypotenuse = short leg (2)`
`long leg = short leg √(3)`

`15 = short leg (2)`
`long leg = (15)/(2) √(3)`

`(15)/(2) = short leg`
`long leg = 12.99`

`7.5 = short leg`

The height of the building is the long leg. 12.99 foot

Answer 2

height of the building is 12.99 feet.

Explanation:

given, try to analyse:

• ladder 15 feet long.
• 60 degree angle to the ground.

the height of the building is opposite to the angle 60° and given hypotenuse, the ladder of 15 feet long.

using sine rule:

`sin(x) = (opposite)/(hypotenuse)`

`sin(60) = (opposite)/(15)`

`opposite = sin(60) *15`

`opposite = 12.99feet`

Therefore the height of the building is 12.99 feet.