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

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 142–√.
The hypotenuse of the second triangle has length 14 Start Root 2 End Root .

The hypotenuse of the second triangle has length 72–√.

Answer 1

In a right triangle with an angle of 45 degrees, the triangle is an isosceles right triangle, meaning the two legs (the sides opposite the 45-degree angles) are of equal length and the length of the hypotenuse can be calculated using the formula:

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

For the second triangle, which has a side opposite the 45-degree angle with a length of 14, we can apply the formula:

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

Thus, the hypotenuse of the second triangle is \(14\sqrt{2}\).

The correct response is:

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