Answer:
See step-by-step explanation.
Step-by-step explanation:
Part 1: Use the law of cosines to find the measure of angle B:
Law of cosines: c^2 = a2 + b2 − 2ab cos(C)
In this case, you're finding b, so b is basically c.
b^2 = a2 + c2 − 2ab cos(b)
b=21 a=22 c=16 (just for now)
21^2 = 22^2+16^2- 2(22)(16) cos (b)
441= 484 + 256 - 704 cos(b)
Measure of angle B= 64.8673
Part 2: Use the law of sines to find the measure of angle C
[tex]\frac{a}{sin (A)}[/tex] =[tex]\frac{b}{sin (B)}[/tex]=[tex]\frac{c}{sin(C)}[/tex]
Using angle b and sides b and c: 43.6121
21/ sin ( 64.8673) = 16/ sin(C)
Measure of angle C = 43.6121
Part 3: Find the measure of angle A
1. The angles in a triangle add up 180.
m<A+m<B+m<C=180
m<A+64.8673 + 43.6121 =180
Measure of angle A=71.5206
Page 2
Part 1: Find the measure of angle B
The angles in a triangle add up 180.
m<A+m<B+m<C=180.
42+ m<B+83=180
Measure of angle B= 55 degrees
Part 2: Use the law of sines to find the length of side a
[tex]\frac{a}{sin (A)}[/tex] =[tex]\frac{b}{sin (B)}[/tex]=[tex]\frac{c}{sin(C)}[/tex]
Length of side a = [tex]\frac{b sin(A)}{sin (B)}[/tex] =[tex]\frac{175 sin(42)}{sin (55)}[/tex]
The length of side a: 142.95
Part 3: Use any method to find the length of side c.
Method= brainpower
aka law of sines:
[tex]c=\frac{a sin (C)}{sin A}[/tex] = [tex]\frac{142.95sin(83)}{sin(42)}[/tex]
c= 212.043
The length of side c: 212.043
