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

Aa^2 + c^2 < b^2
Ba^2 + c^2 > b^2
Cb^2 + c^2 < a^2
Da^2 + b^2 < c^2

Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true? A. a 2 + c 2 lt; b 2 B. a 2 + c 2 gt; b 2 C. class=

Verified Answer :

JeanaShupp

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

\(a^2 + b^2 < c^2\)

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