Question

how high up on a building will 15 foot ladder reach if the foot of the ladder is placed 5 feet from the building? (be sure to include a diagram with your answer)

Answer 1

Use the Pythagorean theorem:
$5^2+x^2=15^2 \\ 25+x^2=225 \\ x^2=225-25 \\ x^2=200 \\ x=\sqrt{200} \\ x=\sqrt{100 \times 2} \\ x=10\sqrt{2} \\ x \approx 14.14$

The ladder will reach approximately 14.14 feet (exactly 10√2 feet) up on the building.