Use a ruler, protractor, and compass to construct, if possible, a triangle with the stated properties. If such a triangle cannot be drawn, explain why. Decide if there can be two or more noncongruent triangles with the stated properties.
-A triangle with angles measuring 11° and 113° and a nonincluded side of length 11 cm
A)Two or more such noncongruent triangles can be constructed.
B)No such triangle can be constructed.
C)Exactly one such triangle can be constructed.

Question

Quizplus · Accepted Answer

The sum of the angles in a triangle is 180°. Given two angles are 11° and 113°, the third angle is 180° - (11° + 113°) = 56°. Since all three angles are known, and one side length is given, exactly one triangle can be constructed. There's no ambiguity in the construction because the angles uniquely determine the shape of the triangle, and the given side length fixes its size.

Use a Ruler, Protractor, and Compass to Construct, If Possible