Mathematics

# A 15-foot ladder is leaning against a 30-foot wall. The bottom end of the ladder is 9 feet from the wall. How many feet above the ground does the ladder touch the wall? Can you help me break it down it's been a while please thanks.

$\alpha ^2 + \beta ^2 = C^2 \\ \\ 9^2 + \beta ^2 = 15^2 \\ \\ 81 + \beta ^2 = 225 \\ \\ => \beta ^2 = 144 \\ \\ => \beta = 12 cm$