Question

A ladder is leaning against the side of a 10m house. If the base of the ladder is 3m away from the house, how tall is the ladder?

Answer 1

The height of the house = 10 m

Base of the ladder is 3 meters away from the house. So base = 3 m

Let us consider that it is a right angle triangle with one side 10 m and base is 3 m. So, we have to find the length of the ladder or the longest leg of the triangle. This can be found by Pythagoras theorem.

Pythagoras theorem is= $a^{2}=b^{2}+c^{2}$

$a^{2}=3^{2}+10^{2}$

= $a^{2}=100+9$

=$a^{2}=109$

or a = 10.44

Hence, the length of the ladder is 10.44 meters.

Please find attached the image of the triangle. We have to find AC.