Question

The base of an 11 foot ladder is 3 feet from a building if the ladder reaches the flat roof how tall is the building

Answer 1

The building, the ladder, and the ground form a right triangle as shown below:

The ladder is the hypotenuse of the triangle and the height H and the horizontal distance (3 ft) are the legs.

Applying the Pythagora's Theorem:

$H^2+3^2=11^2$

Solving for H:

$\begin{gathered} H^2=11^2-3^2 \\ H=\sqrt{11^2-3^2} \\ H=\sqrt[]{121-9} \\ H=\sqrt[]{112} \\ H\approx10.58 \end{gathered}$

The building is 10.58 feet tall