Question

Help with Law of Sines

Answer 1

So i did two problems:
1.Use the Law of Sines to solve (if possible) the triangle for the value of c. Round answers to the nearest tenths. A = 27.5°, a = 15.0 cm, b = 36.4 cm

I got an imaginary number when solving for B. So I answered it no solution

2.Use the Law of Sines to solve (if possible) the triangle for the value of c. Round answers to the nearest tenths. A = 135.3°, a = 14.6 m, b = 18.3 m

When solving for B, I got -17 degrees. I believe that would be no solution as well.

Answer 2

I don't know if that would be correct though

Answer 3

@freckles

Answer 4

How I set up both:

Answer 5

\[B=\sin^{-1}\frac{ 36.4\sin27.5 }{ 15 }\]

Answer 6

Would that look right?

Answer 7

Since 36.4*sin(27.5)/15 = 1.12, which is larger than 1, this means that there are no solutions to sin(B) = 1.12 and no solutions for #1

Answer 8

So the second I would set up

Answer 9

#2

sin(B)/b = sin(A)/a
sin(B)/18.3 = sin(135.3)/14.6
sin(B) = 18.3*sin(135.3)/14.6
sin(B) = 0.88165
B = ???

Answer 10

\[B=\sin^{-1}\frac{ 18.3\sin135.3 }{ 14.6 }\]

Answer 11

I thought you ahve to take arcsin for this?

Answer 12

you do, yes

Answer 13

what do you get for angle B?

Answer 14

1.07935207?

Answer 15

make sure you are in degree mode

Answer 16

in degrees its 61.84

Answer 17

yes

Answer 18

what is angle C?

Answer 19

180-61.84-135.3

Answer 20

yep

Answer 21

I get -17

Answer 22

me too

Answer 23

so this triangle isn't possible either

Answer 24

So i would be right then

Answer 25

you are

Answer 26

Good I just wanted someone to confirm to make sure i wasnt going crazy

Answer 27

"When solving for B, I got -17 degrees."

I think you meant to say "for C"

Answer 28

Indeed that is what i meant lol

Answer 29

Thank you for checking for me :D

Answer 30

you're welcome