Question

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

Answer 1

The true statement about the triangle is (a) b^2 + c^2 > a^2

How to determine the true inequality?

The sides are given as:

a, b and c

The angle opposite of side length a is an acute angle

The above means that:

The side a is the longest side of the triangle.

The Pythagoras theorem states that:

a^2 = b^2 + c^2

Since the triangle is not a right triangle, and the angle opposite a is acute.

Then it means that the square of a is less than the sum of squares of other sides.

This gives

a^2 < b^2 + c^2

Rewrite as:

b^2 + c^2 > a^2

Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2

Read more about triangles at:

brainly.com/question/2515964

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