Question

Determine whether a triangle with these side lengths would be acute, right, or obtuse: 5, 7, and 10;

Answer 1

obtuse

Explanation:

Let 5 = a, 7 = b, 10 = c

if a^2 + b^2 = c^2, then the triangle is a right triangle by the converse of the Pythagorean Theorem

If a^2 + b^2 > c^2, then the triangle is an acute triangle by Theorem 8-4

if a^2 + b^2 < c^2, then the triangle is an obtuse triangle by Theorem 8-3

a^2 = 25

b^2 = 49

c^2 = 100

25 + 49 < 100, therefore the triangle is an obtuse