Question

Marie has a garden in the shape of triangle ABC, for which m∠ A=51°, m∠ B=62° , and m∠ C=67°. Which side of the garden is the longest?

A. overline AB
B. overline BC
C. overline AC
D. Cannot be determined

Answer 1

In triangle ABC with angles measuring 51°, 62°, and 67°, side BC is the longest because it is opposite the largest angle C.Option B is the correct answer.

Step-by-step explanation:

The question asks which side of a triangle garden is the longest, given the measures of its angles. In triangle ABC, the sides opposite the angles are Inverse Proportionate to the angle measures, meaning the side opposite the largest angle is the longest side.

Since m∠C = 67° is the largest angle compared to m∠A = 51° and m∠B = 62°, the side opposite to angle C, which is «line BC», must be the longest. Therefore, the correct answer is B. «line BC».

The inquiry revolves around determining the longest side of triangle ABC based on its angle measures. In a triangle, the sides are inversely proportionate to the angles, signifying that the longest side corresponds to the largest angle. As the largest angle is ∠C with a measure of 67°, the side opposite this angle, denoted as "line BC," is conclusively the longest side in the triangle.

Thus, the accurate answer is B. «line BC», aligning with the principles of triangles and their side-angle relationships.