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

The lengths of the sides are line AB = 22
line AC=12
line BC=16

Answer 1

Answer:

angle B, angle A, angle C

Step-by-step explanation:

The shortest side length will be opposite the smallest angle, and the longest side length will be opposite the largest angle.

When the triangle is drawn and labeled, we see that AB is opposite angle C; BC is opposite angle A; and CA is opposite angle B.

Since the smallest side is AC, this means the smallest angle is angle B.

Since the middle length side is BC, the middle sized angle is A.

Since the longest side is AB, the largest angle is C.

This means the order from smallest to largest is B, A, C.

Answer 2

The angles from smallest to largest is $\boxed{{\text{angleB<angleA<angleC}}}$. Option (b) is correct.

Further explanation:

The angle opposite to the largest side is the largest angle of the triangle.

Given:

The options from smallest to largest are as follows,

(a). angle A, angle B, angle C.

(b). angle B, angle A, angle C.

(c). angle B, angle C, angle A.

(d). angle C, angle A, angle B.

Explanation:

The length of side AB is 22, length of the side AC is 12 and the length of the side BC is 16.

The angle opposite to side AB is angle C, the angle opposite to the side BC is angle A and the angle opposite to the side AC is angle B.

The side AB is largest. Therefore, angle C is the largest.

The side AC is the smallest. Therefore, angle B is the smallest.

Hence, the angles from smallest to largest is $\boxed{{\text{angleC>angleA>angleB}}}$. Option (b) is correct.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Kindly refer to the image attached.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangles

Keywords: Smallest angle, triangle, largest angle, angle A, angle B, angle C, lengths, sides, line, AB = 22, AC = 12, Line BC = 16.