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)

Question

Responses

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 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 142–√.

Answer 1

For a right triangle with an angle of 45 degrees, we can use the properties of 45-45-90 triangles. In such a triangle, the lengths of the legs are equal, and the hypotenuse can be calculated using the formula:

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

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

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

Thus, we can conclude that the hypotenuse of the second triangle has a length of \( 14\sqrt{2} \).

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