Question

problem 15: (first taught in lesson 49) in △abc, m∠a = 49 and m∠b = 18. is overline{bc} or overline{ac} longer? after you enter your answer press go.

Explanation:

Step1: Find the measure of angle \(C\)

The sum of angles in a triangle is \(180^{\circ}\). So, \(m\angle C=180 - 49 - 18=113^{\circ}\).

Step2: Use the side - angle relationship

In a triangle, the larger angle is opposite the longer side.
\(\overline{BC}\) is opposite \(\angle A\) (\(m\angle A = 49^{\circ}\)), and \(\overline{AC}\) is opposite \(\angle B\) (\(m\angle B=18^{\circ}\)). Since \(49>18\), the side opposite the larger angle (\(\angle A\)) is longer.

Answer:

\(\overline{BC}\) is longer.