Question

Question
A right triangle has a hypotenuse of length 102–√
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 142–√
.
The hypotenuse of the second triangle has length 14 Start Root 2 End Root .

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

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 7.

Answer 1

In a right triangle with a 45-degree angle, the sides opposite the 45-degree angles are equal, and the hypotenuse can be calculated using the formula:

\[
\text{Hypotenuse} = \text{side} \times \sqrt{2}
\]

For the first triangle, the length of the side opposite the 45-degree angle is 10. Thus, the hypotenuse \( h_1 \) is given by:

\[
h_1 = 10 \times \sqrt{2}
\]

And according to the problem, it appears that \( h_1 = 102 - \sqrt{} \) is meant to represent that hypotenuse, but it seems incorrectly stated.

Now for the second triangle, the side opposite the 45-degree angle is given as 14. Hence, the hypotenuse \( h_2 \) is calculated as:

\[
h_2 = 14 \times \sqrt{2}
\]

Thus, the length of the hypotenuse in the second triangle is:

\[
14 \sqrt{2}
\]

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