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)

Question

1. The hypotenuse of the second triangle has length 7/2.

2. The hypotenuse of the second triangle has length 14.

3. The hypotenuse of the second triangle has length 14√2.

4. The hypotenuse of the second triangle has length 7.

Answer 1

To solve for the hypotenuse of the second triangle, we will use the properties of right triangles with a 45-degree angle.

In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, and the length of the hypotenuse is \( s \sqrt{2} \), where \( s \) is the length of each leg.

For the second triangle, we are given that the side opposite the 45-degree angle has a length of 14. Since both legs are equal in this triangle:

• Let the length of each leg be \( s = 14 \).

Now we calculate the length of the hypotenuse:

\[ \text{Hypotenuse} = s \sqrt{2} = 14 \sqrt{2} \]

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

The correct option is:

3. The hypotenuse of the second triangle has length 14√2.