One leg of a right triangle is twice the length of the other leg. What is the cosine of the angle between the longer leg and the hypotenuse?

Let x denote the length of the shorter leg. Then the longer leg has length 2x. The hypotenuse of the triangle has length √ (x² + (2x) ²) = √5 x.

The cosine of the angle formed by the longer leg and the hypotenuse is 2x / (√5 x) = 2/√5 = 2√5 / 5

The cosine of the other acute angle is x / (&radc; 5 x) = 1/√5 = √5 / 5