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)

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

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.

Answer 1

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

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

Given the second triangle has a side opposite the 45-degree angle with a length of 14, we can find the hypotenuse as follows:

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

So, the length of the hypotenuse in the second triangle is

\[
14\sqrt{2}
\]

Thus, the answer is:

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