Question

In right triangle ABC, Angle C = 90 degrees, D is a point on AB, and CD is perpendicular to AB. AB = 20 and AD = 5. Find AC

I tried formulas like soacahtoa and Pythagorean theorem but I am unable to figure this out.

Answer 1

nevermind! i had an epiphany

Answer 2

Let AD = x

The Geometric Mean Theorem states that

AD*DB = CD^2
x(20-x) = 25
x = 5(2+√3)

Since right triangles ADC and ACB are similar (Angle A is common to both),

AC/x = 20/AC
AC^2 = 20x = 100(2+√3)
AC = 10√(2+√3) = 5(√2+√6)