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

The hypotenuse of the second triangle has length 4.
The hypotenuse of the second triangle has length 4.

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 42–√
.
The hypotenuse of the second triangle has length 4 Start Root 2 End Root .
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Answer 1

In a 45°–45°–90° triangle the hypotenuse = (leg)·√2. Here the given opposite side is 4√2, so hypotenuse = (4√2)(√2) = 4·2 = 8.