Question

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

The hypotenuse of the second triangle has length 82–√
.
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–√
.
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

Answer: 8.

Reason: For a 45° angle, opposite = hypotenuse·sin45 = hypotenuse·(√2/2). So hypotenuse = opposite·(2/√2) = opposite·√2. With opposite = 4√2, hypotenuse = 4√2·√2 = 4·2 = 8.