Question

Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true?

Answer 1

Answer: D.$a^2 + b^2 < c^2$

Step-by-step explanation:

In the given figure, we have an obtuse triangle which has sides a, b, and c, and the angle opposite the side of length b is obtuse.

∵ In a triangle, the side opposite to the largest angle is largest.

Thus, the largest side in then given obtuse triangle= c

The Pythagorean inequalities theorem says that If a triangle is obtuse than the square of the largest side is greater than the sum of square of other two sides.

Therefore, we have

$a^2 + b^2 < c^2$