Answer:
[tex]c=\sqrt{174}[/tex]
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)
