A right triangle had a hypotenuse of length 82–√

Question

8
2
and an angle of 45°
45
°
, with a side opposite this angle of 8. A second triangle also has an angle of 45°
45
°
, with the side opposite this angle with a length of 12. Determine the length of the hypotenuse in the second triangle. (1 point)
Responses

The hypotenuse of the second triangle is 62–√
6
2
The hypotenuse of the second triangle is 6 square root of 2

The hypotenuse of the second triangle is 6
6
The hypotenuse of the second triangle is 6

The hypotenuse of the second triangle is 12
12
The hypotenuse of the second triangle is 12

The hypotenuse of the second triangle is 122–√

Answer 1

In a right triangle with a 45° angle, the sides opposite the 45° angles are equal, and the relationship between the length of the side opposite the 45° angle \( a \) and the hypotenuse \( c \) can be described using the formula:

\[ c = a \sqrt{2} \]

For the second triangle, the length of the side opposite the 45° angle is given as 12. Therefore, we can calculate the hypotenuse as follows:

\[ c = 12 \sqrt{2} \]

Based on the options provided, it appears that the correct response for the hypotenuse of the second triangle is:

The hypotenuse of the second triangle is 12√2.