Which of the following is the measure of

The answer to your question is 31.4°

Step-by-step explanation:

Data

SR = 54 cm

SQ = 99 cm

RQ = 141 cm

∠QRS = ?

Process

1.- Use the law of cosines to find ∠QRS

          cos QRS = (SQ² - RS² - RQ²) / -2(SR)(RQ)

-Substitution

          cos QRS = (99² - 54² - 141²) / -2(54)(141)

-Simplification

          cos QRS = (9801 - 2916 - 19881) / -15228

          cos QRS = -12996 / -15228

          cos QRS = 0.85343

2.- Find QRS

            ∠QRS = 31.4°

QRS = 31.4°

Step-by-step explanation:

We would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes

QS² = RS² + QR² - 2(RS × QR)CosR

99² = 54² + 141² - 2(54 × 141)CosR

9801 = 2916 + 19881 - 15228CosR

9801 = 22979 - 15228CosR

15228CosR = 22979 - 9801

15228CosR = 12996

CosR = 12996/15228

CosR = 0.853

R = Cos^(- 1)0.853

R = 31.4°

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

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