Question

A fireman's ladder reaches 13.9 m up a building. The ladder is propped up by a support, placed 5.4 m from the building and 3.6 m from the base of the ladder. If the support is L meters long, solve for L. Round your answer to 1 decimal place.

Answer 1

Explanation:

The right angle triangle ABC that the ladder forms with the wall is shown in the attached photo.

Triangle ABC and triangle EBD are similar triangles. This means that AC/ED = EB/AB

AB = 5.4 + 3.6 = 9 meters

AC = 13.9 meters

ED = L meters

EB = 3.6 meters

Therefore,

3.6/9 = L/13.9

Cross multiplying, it becomes

9 × L = 13.9 × 3.6

9L = 50.04

L = 50.04/9 = 5.56

Rounding up to 1 decimal place,

L = 5.6 meters