A right triangle has a hypotenuse of length 16 and an angle of 45°, with a side opposite this angle of length 8 √ 2. A second right triangle also has an angle of 45° and a side opposite this angle with a length of 4√ 2. Determine the length of the hypotenuse in the second triangle.

Question

(1 point)
A. The hypotenuse of the second triangle has length 4.
B. The hypotenuse of the second triangle has length 8.
C. The hypotenuse of the second triangle has length 4√2.
D. The hypotenuse of the second triangle has length 8√2

Answer 1

In a right triangle with angles of 45°, the sides opposite the 45° angles are equal, and the relationship between the side lengths and the hypotenuse can be expressed using the following relation:

If the length of the side opposite the 45° angle is \( x \), then the hypotenuse \( h \) is given by:

\[ h = x \sqrt{2} \]

For the second triangle you mentioned, the side opposite the 45° angle has a length of \( 4\sqrt{2} \).

Using the formula, we can find the hypotenuse:

\[ h = (4\sqrt{2}) \sqrt{2} = 4 \cdot 2 = 8 \]

Thus, the length of the hypotenuse in the second triangle is \( 8 \).

The correct answer is: B. The hypotenuse of the second triangle has length 8.