What is the length of NP?

Step-by-step explanation:

First, find the length of MP. This can be done with the Pythagorean Theorem.

We can use x as angle MP.

a² + b² = c²

10²+ 7² = x²

100 + 49 = x²

x² = 149

Take the square root to get

x = √(149)

Now do the Pythagorean Theorem for Triangle MNP. We can again use x for angle NP.

a² + b² = c²

5² + √(149)² = c²

25 + 149 = c²

c² = 174

c = √(174)