Problem: In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:
Answer Choices:
A. 15∘
B. 30∘
C. 45∘
D. 60∘
E. 75∘
Solution:
c2=2ab∴a2+b2=2ab∴(a−b)2=0∴a=b Since the right triangle is isosceles, one of the acute angles is 45∘.