Question

A right triangle has a hypotenuse of length 10√2 and an angle of 45 degrees, with a side opposite this angle with a length of 10. A second right triangle also has an angle of 45 degrees, with a side opposite this angle with a length of 14. Determine the length of the hypotenuse in the second triangle.(1 point) Responses The hypotenuse of the second triangle has length 72–√ . The hypotenuse of the second triangle has length 7 Start Root 2 End Root . The hypotenuse of the second triangle has length 14. The hypotenuse of the second triangle has length 14. The hypotenuse of the second triangle has length 7. The hypotenuse of the second triangle has length 7. The hypotenuse of the second triangle has length 142–√ . The hypotenuse of the second triangle has length 14 Start Root 2 End Root .

Answer 1

In a right triangle with an angle of 45 degrees, the sides opposite the 45-degree angles are equal, and the hypotenuse can be calculated using the relationship between the side lengths.

For a right triangle where one side (the side opposite the 45-degree angle) is \( x \), the hypotenuse \( h \) can be found using the formula:

\[ h = x\sqrt{2} \]

In the second right triangle, the side opposite the 45-degree angle has a length of 14. Therefore, we can calculate the hypotenuse:

\[ h = 14\sqrt{2} \]

Thus, the length of the hypotenuse in the second triangle is \( 14\sqrt{2} \).

Now, verifying against the provided multiple choice responses, the correct answer is:

The hypotenuse of the second triangle has length \( 14\sqrt{2} \).