Question

Solve the triangle.

A = 32°, a = 19, b = 12

Answer 1

Remember the law of sines....a/A = b/B = c/C

so if 32/19 is A
then 32/19 = x/12

after that...you'll have 2 of the 3 angles...with that...you know that the angles of a triangle add up to what?

Answer 2

180 Degrees

Answer 3

correct...so now...for A
to correct myself as well

side A divided by the sin of angle A means what?

Answer 4

I'm not sure..

Answer 5

the law of sines....means you take...

\[a/\sin A=b/\sin B=c/\sin C\]

Answer 6

where a, b, and c are side lengths...and A, B, and C are angles

Answer 7

so for the first part.... a/sinA....what is your a and what is your A?

Answer 8

A=32 a=19

Answer 9

correct...so now to solve that...you calculate.....
\[19/\sin 32\]

Answer 10

so thats about35.85

Answer 11

correct...so now for the second part...we know what b is...but not what B is....so in the equation...b/sinB....it is 12/sinB

remember how you just got 35.85?

35.85 is a/sinA right? looking at the law of sines now...we have

35.85 = 12/sinB

how do we solve for sinB?

Answer 12

I also found the Sin of B to be 2.9 by setting the 19/sin32=12/sinB

Answer 13

hmmm lets look at your calculation for a second....

\[19/\sin32 = 12/sinB\]

to solve for sinB...we multiply both sides of the equation by sinB...then dividie both sides by 19/sin32 to isolate sinB

so we have sinB = 12/19sin32

Answer 14

but do we WANT sinB? no we want B.....so how do we isolate B? we take the inverse sin of whatever answer you get for 12/19sin32

Answer 15

Im not sure how to make the inverse of 0.3483

Answer 16

....do you have a calculator on you? if so..just do the second button and press sin...most likely the same for many calculators

Answer 17

oh, i apologize, i could use the arcsine, i just did'nt think about that one. sorry

Answer 18

no problem :) okay so what do you get from that?

Answer 19

I found that to be .3557

Answer 20

make sure your calculator is in degree mode and not radian mode

Answer 21

got it! 20.382

Answer 22

there you go :) okay....so thats your angle B correct?

Answer 23

yes!. so from there I can find the others using the same method?

Answer 24

precisely....remembering to find the third angle....180 - the 2 you already found

Answer 25

got it. thanks so much.

Answer 26

anytime :) let me know what you end up with

Answer 27

B=20.38, C=127.6, c=27.3

Answer 28

with the rounding you were using...you are correct :)