Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC=20 and DC=6, what is the length of BC? (Note: the figure is not drawn to scale.)
+129845 A
14
20
D
6
B C
Since BD is an altitude....angles BDA and BDC are right angles......so triangles BDA and BDC are right triangles
BD^2 = AB^2 - 14^2 ( 1)
BD^2 = BC^2 - 6^2 (2) subtract (1) from (2)
BC^2 - AB^2 = 14^2 - 6^2
BC^2 - AB^2 = 160
AB^2 = BC^2 - 160
So....by the Pythagorean Theorem
AB^2 + BC^2 = AC^2
(BC^2 - 160) + BC^2 = 20^2
2BC^2 - 160 = 400
2BC^2 = 560
BC^2 = 280
BC = sqrt (280) = 2sqrt (70) ≈ 16.733
