Question

Analyze the diagram below and answer the question that follows.

In the triangle above, which angle is smallest in measure?

A. angle A
B. angle B
C. angle C
D. all three sides are congruent

Answer 1

According to the Law of Cosines, angle A would be 55.78, angle B would be 64.12, and angle C would be 60.10. Therefore, the answer would be angle A. Hope this helps!

~Ash

Answer 2

Answer: The correct option is (A) angle A.

Step-by-step explanation: We are given to analyze the diagram and to select the angle in triangle ABC that is smallest in measure.

From the diagram, we note that in triangle ABC, the lengths of the three sides are

AB = 29.87 units, BC = 28.49 units and CA = 31 units.

So, the descending order of the lengths of the three sides is

`31 > 29.87 > 28.49\\\\\Rightarrow CA > AB > BC.`

We know that

the angle opposite to a smaller side of the triangle is smaller and the angle opposite to a greater side is greater.

Angle opposite to side CA is ∠B,

Angle opposite to side AB is ∠C

and

Angle opposite to side BC is ∠A.

So, we get

`CA > AB > BC\\\\\Rightarrow m\angle B>m\angle C>m\angle A.`

Thus, the angle A is smallest in measure.

Option (A) is CORRECT.