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

Question

olga2289 [7]

3 years ago

6

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?

History

1 answer:

viktelen [127] · Answer 1 · 2022-04-05T08:19:56+03:00

<span>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</span>