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?

Answer 1

12 foot 6 inches

Background

There are several ways this can be calculated. But first it is helpful to know something interesting about triangles!

If the three internal angles of a triangle are the same as the internal angles of another triangle, both triangles are said to be 'similar', even though one may be bigger than the other. If this is so, then the proprtionate lengths of the sides in one triangle will be the same as the proportionate lengths of the sides of the other triangle.

For examle, if the longest side of triangle 'A' is twice as long as its shortest side, then this ratio will also be true for triangle 'B'.

Some methods

* In the question, in scenario 'A' the longest side is 6 ft, and the triangle height is 5 ft. In scenario 'B' the longest side is 15 ft, which is 2.5 times bigger than scenario 'A', so the new height will also be 2.5 bigger than it was. It was 5 ft, so now it will be 2.5 x 5 = 12.5 ft. * Another way to work it out: The height was 5/6ths of the ladder length. The new ladder length is 15 ft, so the new height will be 15 x 5/6 = 12.5 ft