Question

a triangular garden has sides of length 10 feet, 15 feet, and 12 feet. if the angles opposite these sides are a, b, and c respectively, which of the following is the correct order of the angles from largest to smallest? a) ∠a > ∠b > ∠c b) ∠b > ∠c > ∠a c) ∠c > ∠a > ∠b d) ∠b > ∠a > ∠c your answer in triangle abc, angle a measures 40°, angle b measures 80°, and angle c measures 60°. which side of the triangle is the longest? a) ab b) bc c) ac d) cannot be determined

Explanation:

Step1: Recall angle - side relationship

In a triangle, the largest angle is opposite the longest side and the smallest angle is opposite the shortest side.

Step2: Analyze first question

The side lengths are 10, 12, and 15. The longest side is 15 (opposite angle B), the next - longest is 12 (opposite angle C), and the shortest is 10 (opposite angle A). So, $\angle B>\angle C>\angle A$.

Step3: Analyze second question

The angles are $\angle A = 40^{\circ}$, $\angle B=80^{\circ}$, $\angle C = 60^{\circ}$. The largest angle is $\angle B$. The side opposite $\angle B$ is $AC$. So, side $AC$ is the longest.

Answer:

1. b) $\angle B>\angle C>\angle A$
2. c) $AC$