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?
The heigt is
Here's a simple sketch of your problem:
In both cases, your angle
The ladder, the ground and the building build a right-angle triangle where the respective ladder is the hypotenuse.
We know that
Thus, in the case of the
#sin alpha = 5/6#
#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"#