Question

In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find: a Find CD, if BC = 3 in

Answer 1

CD = (3/2)√2

Explanation:

All the triangles are similar isosceles right triangles, so the hypotenuse in each case is √(1²+1²) = √2 times the length of the corresponding legs. BC is the hypotenuse of ΔBCD, so leg CD is that length divided by √2.

CD = BC/√2 = 3/√2

CD = (3/2)√2