Question

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

A. a^2+b^2<c^2

Answer 1

When a triangle is obtuse, the length of c^2 is bigger than the combined lengths of a^2 and b^2.

a^2+b^2<c^2

"A" is the best answer.

I hope this helps!
~kaikers

Answer 2

Answer:  The correct option is (C). $b^2+c^2<a^2.$

Step-by-step explanation:  Given that a triangle has sides of lengths a, b and c. And, the angle opposite the side of length 'a' is obtuse.

We are to select the correct statement from the given options.

We know that

In an OBTUSE-ANGLED triangle,  the square of the length of the largest side is greater than the sum of the squares of the lengths of two smaller sides.

The largest side is the one which is opposite to the obtuse angle of the triangle.

In the given triangle, the obtuse angle is the angle that is opposite to the side of length 'a'.

So, the largest side is of length 'a'.

Therefore, the square of 'a' will be greater than the sum of the squares of 'b' and 'c'.

That is,

$a^2>b^2+c^2\\\\\Rightarrow b^2+c^2<a^2.$

Thus, (C) is the correct option.