Question

Use the Law of Sines to find the missing angle of the triangle. Find angle B given that C = 83, A = 44, and angle A = 31.

A. 2.7°

B. 15.8°

C. 164.2°

D. 76.3°

Answer 1

∠C = arcsin(83/44*sin(31°)) = 76.3°

∠B = 180° -31° -76.3° = 72.7° . . . . . . . probably matches selection A

_____
There is another solution:
∠C = 180° -76.3° = 103.7°

∠B = 180° -103.7° -31° = 45.3° . . . . . not an offered choice

Answer 2

Answer:

Option D is correct

Step-by-step explanation:

Sine rule is

$\frac{sinC}{c}= \frac{sinA}{a} = \frac{sinB}{b}$

we have c =83 , a =44 And A =31 degrees

$\frac{sinC}{c} =\frac{sinA}{a} \\\frac{sinC}{83} =\frac{sin31}{44} \\sinC=83X(\frac{0.515}{44} )\\sinC =0.9716\\C =76.3$ or 103.3

If C = 76.3 degrees  or  C =103.3  and A = 31 degrees

Using triangle angle sum property

A+B+C = 180

31+76.3 +B = 180

B=180 -31-76.3

B= 72.7

when C =103.3

then B = 180- 31-103.3

       B = 45.7

According to options given ,Its asking for Angle C and which is 76.3