Question

"In right triangle NPQ, angle P is the right angle, angle Q = 65 degrees, and QP = 10. What is the measure of the hypotenuse?

A. 45.1
B. 21.4
C. 10
D. 23.7"

Answer 1

The measure of the hypotenuse is approximately 14.14.

Step-by-step explanation:

In a right triangle, the hypotenuse is the side opposite the right angle. To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we can solve for the length of the hypotenuse:

`c^2 = a^2 + b^2`

`c^2 = 10^2 + (QP)^2`

`c^2 = 10^2 + 10^2`

`c^2 = 100 + 100`

`c^2 = 200`

`c = √(200)`

≈ 14.14

Therefore, the measure of the hypotenuse is approximately 14.14.