A right triangle has a hypotenuse of length 102–√

Question

10
2
and an angle of 45 degrees, with a side opposite this angle with a length of 10. A second right triangle also has an angle of 45 degrees, with a side opposite this angle with a length of 14. Determine the length of the hypotenuse in the second triangle.(1 point)
Responses

The hypotenuse of the second triangle has length 7.
The hypotenuse of the second triangle has length 7.

The hypotenuse of the second triangle has length 14.
The hypotenuse of the second triangle has length 14.

The hypotenuse of the second triangle has length 72–√
7
2
.
The hypotenuse of the second triangle has length 7 Start Root 2 End Root .

The hypotenuse of the second triangle has length 142–√
14

Answer 1

In a right triangle with a 45-degree angle, the two legs are equal in length, and they are related to the hypotenuse by the formula:

\[ \text{Hypotenuse} = \text{leg length} \cdot \sqrt{2} \]

For the second triangle, where the side opposite the 45-degree angle has a length of 14, the calculation of the hypotenuse will be:

\[ \text{Hypotenuse} = 14 \cdot \sqrt{2} \]

So, the hypotenuse of the second triangle has length \( 14\sqrt{2} \).

Thus, the correct response is:

The hypotenuse of the second triangle has length \( 14\sqrt{2} \).