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.
