Question

A 20 foot ladder rests against the top of a 15 foot building. How far does the ladder extend from the base of the wall and what angle does the ladder make with the ground?

Answer 1

Look at the picture.

Calculate x using the Pythagorean theorem:
$x^2+15^2=20^2 \\ x^2+225=400 \\ x^2=400-225 \\ x^2=175 \\ x=\sqrt{175} \\ x=\sqrt{25 \times 7} \\ x=5\sqrt{7} \\ x \approx 13.23$

Calculate α using sine:
$\sin \alpha =\frac{15}{20} \\ \sin \alpha= 0.7500 \\ \alpha \approx 49^\circ$

The ladder extends approximately 13.23 feet (exactly: 5√7 feet) from the base of the wall and makes an approximately 49° angle with the ground.