A 6-foot ladder touches the side of a building at a point 5 feet above the ground. At what height would a 15-foot ladder touch the building if it makes the same angle with the ground as the shorter ladder?

1 Answer
Feb 3, 2016

The heigt is #12.5# foot.


Here's a simple sketch of your problem:

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In both cases, your angle #alpha# is the same.

The ladder, the ground and the building build a right-angle triangle where the respective ladder is the hypotenuse.

We know that #sin# of an angle can be computed as the opposite side divided by the hypotenuse.

Thus, in the case of the #6#-foot ladder, we have:

#sin alpha = 5/6#

For the #15#-foot ladder, we have

#sin alpha = x / 15#

However, the angles are the same. Thus, we get

#5/6 = x / 15 " "<=>" " x = 5/6 * 15 = 75/6 = 12.5 " foot"#