Question

Use the law of Cosines to solve the triangle.

B=12º, a=32, c=36

Answer 1

So we just need to plug some numbers into the equation for the law of cosines and go from there. Now I can choose to rearrange the formula in different ways as long as you do it properly. So I'll list the formula like this and see if you can plug the appropriate numbers in and solve for the angle

Answer 2

ok

Answer 3

\[a ^{2} = b ^{2} + c ^{2} - 2ac(\cos A)\]

Answer 4

32^2= b^2=36^2

Answer 5

i mean + after b^2

Answer 6

but i dont have cos A

Answer 7

You need to solve for cos A. You can fill in all the information and eventually be left with something = cosA

Answer 8

\[32^{2} = 12^{2} + 36^{2} -2(12)(36)(cosA)\]
First solve for cosA = something and we'll go from there :3

Answer 9

is it 448?

Answer 10

If done corrwctly, you should get \[\frac{ 13 }{ 27 } \]

Answer 11

as the final answer?

Answer 12

Im sorry, it got cut off, it shouldve said 13/27 = cosA

Answer 13

Do you know how to solve for cosA from here?

Answer 14

what are they exactly asking to do ?

Answer 15

They want you to find angles A, B, and C. When they give you lower case letters, these refer to the sides of a triangle. Upper case letters refer to angles. So solving a triangle is having all 3 sides and all 3 angles. In this case you had all 3 sides but no angles. so we're trying to find the 3 angles. So right now, we need A. We've made it up to cosA = 13/27, now we just need to get A. Any idea how to do that?

Answer 16

do we use the inverse of cosine?

Answer 17

Exactly.

Answer 18

is it tan^-1 pop/adj?

Answer 19

i mean opp srry

Answer 20

Well, this is a calculator question really. You would need to do:

\[\cos^{-1} (\frac{ 13 }{ 27 }) = \theta \]

Answer 21

oh ok got it

Answer 22

Yep. So what'd we getfor theta?

Answer 23

whats the formula for the law of sines?

61.21

Answer 24

Sorry about that. And yes, 61.21. From there, the formula is:

\[\frac{ a }{ sinA } = \frac{ b }{ sinB } = \frac{ c }{ sinC }\]

Answer 25

how do we proceed after this?

Answer 26

Well, we have an angle A and a side a, so this allows us to use this information to solve for either of the other two angles. If I wanted to solve for B first, I would do:

\[\frac{ 32 }{ \sin(61.21) } = \frac{ 12 }{ sinB }\]
from here we can solve for sinB and, once again, take the inverse once we finish.

Answer 27

how doe we solve for sin B?

Answer 28

If we have equivalent fractions then this means we can cross multiply and eventually get sinB by itself.

Answer 29

got it