Question

A painter sets a ladder up to reach the bottom of a second storey window 16 feet above the ground. The base of the ladder is 12 feet from the house. While the painter mixes the paint a neighbour's dog bumps the ladder which moves the base 2 feet farther away from the house. How far up side of the house does the ladder reach?

Answer 1

In $△PBC$

$PB=12ft$

$BC=16ft$

$\therefore PC=\sqrt{{12}^2+{16}^2}$ (By pythogoras theorem)

$PC=\sqrt{144+256}$

$PC=\sqrt{400}$

$PC=20ft$

length of ladder $=20ft$

Now in $△ABM$

$AM=20ft$ (length of ladder)

$AB=14ft$

$\therefore BM=\sqrt{{AM}^2-{AB}^2}$

$BM=\sqrt{400-196}=\sqrt{201}$

$BM=14.2ft$