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

Answer:

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

Step-by-step 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.  

$hypotenuse = short leg (2)$                          $long leg = short leg \sqrt{3}$  

$15 = short leg (2)$                                        $long leg = \frac{15}{2} \sqrt{3}$  

$\frac{15}{2} = short leg$                                             $long leg = 12.99$

$7.5 = short leg$

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

Answer 2

Answer:

height of the building is 12.99 feet.

Step-by-step 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:

$sin(x) = \frac{opposite}{hypotenuse}$

$sin(60) = \frac{opposite}{15}$

$opposite = sin(60) *15$

$opposite = 12.99feet$

Therefore the height of the building is 12.99 feet.