Question

A right triangle has a hypotenuse of length 16 and an angle of 45°, with a side opposite this angle of length 82–√
8
2
. A second right triangle also has an angle of 45° and a side opposite this angle with a length of 42–√
4
2
. Determine the length of the hypotenuse in the second triangle.(1 point)
Responses

The hypotenuse of the second triangle has length 82–√
8
2
.
The hypotenuse of the second triangle has length 8 Start Root 2 End Root .

The hypotenuse of the second triangle has length 8.
The hypotenuse of the second triangle has length 8.

The hypotenuse of the second triangle has length 42–√
4
2
.
The hypotenuse of the second triangle has length 4 Start Root 2 End Root .

The hypotenuse of the second triangle has length 4.

Answer 1

In a 45°-45°-90° triangle the hypotenuse = leg × √2. With leg = 4√2, hypotenuse = (4√2)·√2 = 4·2 = 8.

So the hypotenuse of the second triangle is 8.