Use the Pythagorean theorem:
[tex]5^2+x^2=15^2 \\
25+x^2=225 \\
x^2=225-25 \\
x^2=200 \\
x=\sqrt{200} \\
x=\sqrt{100 \times 2} \\
x=10\sqrt{2} \\
x \approx 14.14[/tex]
The ladder will reach approximately 14.14 feet (exactly 10√2 feet) up on the building.
