Question

A right triangle has a hypotenuse of length 16 and an angle of 45°, with a side opposite this angle of length $8\sqrt{2}$. A second right triangle also has an angle of 45° and a side opposite this angle with a length of $4\sqrt{2}$. Determine the length of the hypotenuse in the second triangle.AnswersThe hypotenuse of the second triangle has length 4.The hypotenuse of the second triangle has length $8\sqrt{2}$.The hypotenuse of the second triangle has length 8.The hypotenuse of the second triangle has length $4\sqrt{2}$.

Answer 1

In a 45°-45°-90° triangle the hypotenuse = (leg)·√2. So for the second triangle hypotenuse = (4√2)·√2 = 4·2 = 8.

Answer: The hypotenuse has length 8.