Question

How to find the sides and angle of these two problems

Answer 1

See step-by-step explanation.

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

`(a)/(sin (A))` =
`(b)/(sin (B))`=
`(c)/(sin(C))`

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

`(a)/(sin (A))` =
`(b)/(sin (B))`=
`(c)/(sin(C))`

Length of side a =
`(b sin(A))/(sin (B))` =
`(175 sin(42))/(sin (55))`

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:

`c=(a sin (C))/(sin A)` =
`(142.95sin(83))/(sin(42))`

c= 212.043

The length of side c: 212.043