Question

In △ABC (not shown), AB=6, BC=9, and AC=13. Name the smallest angle of △ABC.

a) ∠C
b) ∠B
c) ∠A

Answer 1

The smallest angle of ΔABC is Angle B with a measure of approximately 30.1°.

Step-by-step explanation:

To name the smallest angle of ∇ABC, we need to compare the three angles of the triangle. Using the Law of Cosines, we can determine the measure of each angle. According to the formula c^2 = a^2 + b^2 - 2abcos(C), where c is the side opposite angle C, a is the side opposite angle A, and b is the side opposite angle B, we can calculate the angles as follows:

1. Angle A = acos((b^2 + c^2 - a^2) / (2bc))
2. Angle B = acos((a^2 + c^2 - b^2) / (2ac))
3. Angle C = acos((a^2 + b^2 - c^2) / (2ab))

Using the given values, substituting them into the formulas, and calculating the angles, we find:

Angle A ≈ 48.7°

Angle B ≈ 30.1°

Angle C ≈ 101.2°

Therefore, the smallest angle of ∇ABC is Angle B with a measure of approximately 30.1°, so the correct answer is b) ∠B.