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 42–√ .
The hypotenuse of the second triangle has length 4 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 4.

Answer 1

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

Answer: The hypotenuse is 8.