Video Transcript
Which of the following inequalities describes the angles of the triangle 𝐴𝐵𝐶? Option (A) the measure of angle 𝐴 is greater than the measure of angle 𝐵 is greater than the measure of angle 𝐶. Option (B) the measure of angle 𝐵 is greater than the measure of angle 𝐶 is greater than the measure of angle 𝐴. Option (C) the measure of angle 𝐶 is greater than the measure of angle 𝐴 is greater than the measure of angle 𝐵. Option (D) the measure of angle 𝐵 is greater than the measure of angle 𝐴 is greater than the measure of angle 𝐶. Or is it option (E) the measure of angle 𝐶 is greater than the measure of angle 𝐵 is greater than the measure of angle 𝐴?
In this question, we are given all three side lengths in a triangle. And we are asked to use this determine the correct inequalities describing the measures of the internal angles in the triangle. We can do this by recalling that we can compare the measures of the internal angles in a triangle from its side lengths by applying the angle comparison theorem in triangles. In general, we know that the angles of larger measure must be opposite the longer sides in a triangle. So if 𝑥 is greater than 𝑦 is greater than 𝑧 in a triangle 𝑋𝑌𝑍, then the angle at 𝑋 is larger than the angle at 𝑌 is larger than the angle at 𝑍.
In the figure, we can see that the side opposite vertex 𝐵 is the longest at 14 centimeters, followed by the side opposite vertex 𝐴 at 10 centimeters. Finally, the side opposite vertex 𝐶 is the shortest at eight centimeters. Since the angles of larger measure are opposite the longer sides in a triangle, this tells us that the measure of angle 𝐵 is greater than the measure of angle 𝐴 is greater than the measure of angle 𝐶, which we see matches option (D).
