Question

a student draws the figure to the right. explain why the figure cannot have the labeled dimensions. then describe a way to change the dimensions to make the figure possible. figure not drawn to scale. which of the following correctly explains why the figure cannot have the labeled dimensions? a. the longer third side is opposite the larger included angle. b. the longer third side is opposite the smaller included angle. c. the shorter third side is opposite the smaller included angle. d. none of the explanations are correct.

Explanation:

In a triangle, the larger side is opposite the larger angle (and vice versa) by the triangle side - angle relationship. Here, we have two triangles formed (the parallelogram is split into two triangles). One angle is \(87^{\circ}\) and the other is \(84^{\circ}\). The side opposite \(84^{\circ}\) is 13, and the side opposite \(87^{\circ}\) is 11. Since \(87^{\circ}>84^{\circ}\), the side opposite \(87^{\circ}\) should be longer than the side opposite \(84^{\circ}\), but 11 < 13. So the longer third side (13) is opposite the smaller included angle (\(84^{\circ}\)), which is option B.

Answer:

B. The longer third side is opposite the smaller included angle.