Question

A right triangle has a hypotenuse of length 102–√
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 142–√
14
2
The hypotenuse of the second triangle has length 14 square root of 2

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 square root of 2

Answer 1

In a 45°–45°–90° triangle, the hypotenuse = leg × √2. For the second triangle with leg 14, hypotenuse = 14√2.

So the correct choice is: The hypotenuse of the second triangle has length 14√2.