Question

Consider the triangle.

Which shows the order of the angles from smallest to
largest?

•angle A, angle B, angle C
•angle B, angle A, angle C
•angle B, angle C, angle A
•angle C, angle A, angle B

Answer 1

•angle B, angle A, angle C

Answer 2

angle B, angle A, angle C

Explanation:

Given triangle ABC,

Where, length side of AB = 22

side BC = 16

side AC = 12

We can determine the order of the angles of the triangle without any calculation bearing in mind that each angle would correspond with the sides opposite each of them.

What this means is that, the larger the length of the side, the larger the angle opposite it, while the smaller the length of the side, the smaller the angle opposite it would be.

Now let's order our angles judging by the length of the sides opposite each of them.

Angle A is opposite side BC (16)

Angle B is opposite side AC (12)

Angle C is opposite side AB (22)

There, the largest angle would be the angle with the largest side opposite it = angle C, followed by angle A, and angle B, which is the smallest angle with the smallest side length opposite it.

Angle B < angle A < angle C

The answer is: angle B, angle A, angle C