Question

How long must a ladder be if it is to be leaned against a house at a point 9 ft above the ground resting 3 ft from the bottom edge of the wall?

Answer 1

Answer:

9.5 feet

Step-by-step explanation:

We have that,

Height of the point at the wall where the ladder is leaned = 9 feet

Horizontal distance between the ladder and wall = 3 feet.

So, we get the right triangle as shown in the figure.

Using 'Pythagoras Theorem', i.e. $hypotenuse^{2}=perpendicular^{2}+base^{2}$, we get,

$x^{2}=9^{2}+3^{2}$

i.e. $x^{2}=81+9$

i.e. $x^{2}=90$

i.e. x = 9.5 feet.

Thus, the length of the ladder must be 9.5 feet.