Question

Solve the triangle.

B = 72°, b = 12, c = 8

Answer 1

do you know the Law of Sines?

Answer 2

a/sinA=b/sinB=c/sinB

Answer 3

shoot i messed up, the order is wrong

Answer 4

yes @gloves exactly. now only looking at the b/sinB = c/sinC part, how do you think you could plug in the numbers you are given?

Answer 5

yea @dumbcow i was going to say i wouldnt recommend the law of cosines here

Answer 6

12/sin72=8/sinC

Answer 7

perfect now, can you cross multiply that?

Answer 8

8(sin72)=12(sinC)

Answer 9

try multiplying 8 and sin72

Answer 10

7.6

Answer 11

yes but you can use the knowledge that a triangle has 180 degrees and subtract

Answer 12

now divide that number by 12

Answer 13

yeah i had a dumb moment

Answer 14

180-72=108

Answer 15

and divid 108 by 12?

Answer 16

divide*

Answer 17

for now just divide 7.6 by 12. you should get some annoying decimal, but i will make it make sense

Answer 18

0.633

Answer 19

alright now do you know that inverse sines are the opposite of sines the way multiplication is the opposite of division?

Answer 20

yeah

Answer 21

perfect, then inverse sine your 0.633

Answer 22

you should get something that may also be a decimal. if so, just round it up to the nearest whole number

Answer 23

39.27degrees

Answer 24

i would round that to just 39 degrees

Answer 25

alright so is that my angle for c

Answer 26

now you have, 72 degrees as angle B, 39 degrees as angle C, and now we go back to addition and subtraction

Answer 27

triangle=180 degrees. how do you find angle A?

Answer 28

69

Answer 29

180-39-72

Answer 30

yep perfect now you have angle A. look back to your Law of sines and look now at the a/SinA=b/SinB part how can you plug what you have into that?

Answer 31

a/sin69=12/sin72

Answer 32

awesome now for this part id say just multiply the 12 by sin69 as like halfway cross multiplying and the reason for that is then you make this a 1 step problem. 12(sin69)/sin72 = a

Answer 33

11

Answer 34

perfect, there you go

Answer 35

so side a=11 b=12 c=8
A=69, B=72 C=39

Answer 36

@TechnoSoul thank you so miuch for your help