Question

A right triangle has a hypotenuse of length 102–√ 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)

Answer 1

To determine the length of the hypotenuse in the second right triangle, we can use the properties of 45-degree angles in right triangles.

In a right triangle with a 45-degree angle, the sides opposite the 45-degree angles (let's call them \(a\)) are equal, and both sides are equal to each other. The hypotenuse \(c\) can be calculated using the formula:

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

For the second triangle, where the side opposite the 45-degree angle has a length of 14, we can substitute \(a = 14\) into the formula:

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

Therefore, the length of the hypotenuse in the second triangle is:

\[ \boxed{14\sqrt{2}} \]