Question

the base of a 15 ft ladder is 12 feet from the base of a building. a 25 foot ladder rests against the building at the same angle. how high up the wall does the 25 foot ladder reach

Answer 1

The ladder reaches
`15ft`

Explanation:

In the first case we have

`cos\theta =(12)/(15)`

In second case let the height be
`x`

We have

`sin\theta =(x)/(25)`

We know that

`cos\theta =(12)/(15)\\\\sin\theta =\sqrt{1-(12^(2))/(15^(2)) } \\\\sin\theta =\sqrt{(81)/(225) } \\\\sin\theta =(9)/(15) }`

Substituting

`(9)/(15) =(x)/(25)\\\\x=(25*9)/(15) =15`

The ladder reaches
`15ft`