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19 votes
19 votes
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?

User George Host
by
2.1k points

2 Answers

22 votes
22 votes

Answer:

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

User Vdogsandman
by
2.9k points
18 votes
18 votes

Answer:

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.

User Ankit Bhardwaj
by
2.9k points
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