In △ ABC, ∠ ACB = 90, CD is the height of edge AB, AC = 15, BC = 20, find the length of AD and BD

In △ ABC, ∠ ACB = 90, CD is the height of edge AB, AC = 15, BC = 20, find the length of AD and BD

∵∠ACB=90°
‖ AC ^ 2 + BC ^ 2 = AB ^ 2 (Pythagorean theorem)
∵AC=15,BC=20
∴AB=25
∵ CD is the height of edge ab
∴S△ABC=1/2×AC×BC=1/2×AB×CD
∴15×20=25×CD
∴CD=12
∵∠ADC=90°
| ad ^ 2 + CD ^ 2 = AC ^ 2 (Pythagorean theorem)
∵CD=12,AC=15
∴AD=9
∴BD=AB-AD=25-9=16