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

Answer:

The ladder reaches $15ft$

Step-by-step explanation:

In the first case we have

$cos\theta =\frac{12}{15}$

In second case let the height be $x$

We have

$sin\theta =\frac{x}{25}$

We know that

$cos\theta =\frac{12}{15}\\\\sin\theta =\sqrt{1-\frac{12^{2}}{15^{2}} } \\\\sin\theta =\sqrt{\frac{81}{225} } \\\\sin\theta =\frac{9}{15} }$

Substituting

$\frac{9}{15} =\frac{x}{25}\\\\x=\frac{25\times9}{15} =15$

The ladder reaches $15ft$