Question

Law of cosines help?

Answer 1

Find the area of the triangle with the given measurements.
B = 105, a = 12 cm, c = 19 cm

Answer 2

Okay, so do you know the law of cosines formulas?

Answer 3

Yes

Answer 4

You're going to need to use Heron's formula for this.

Answer 5

Yep, I need to find the side length b right?

Answer 6

Correct.

Answer 7

Use law of cosines first to find b. Then use Heron's formula.

Answer 8

Ok, I get Heron's area formula, but I'm not sure how to get the 3rd side length.

Answer 9

\[b^2 = 12^2 + 19^2-2*12*19*\cos(105)\]

Answer 10

Law of cosines:
\(\large b^2=a^2+c^2-2ac\cos B\)
Plug in and solve for b.

Answer 11

\(\sf b^2~=~12^2~+~19^2~-~2ac~cosB\)

Answer 12

You know B.

Answer 13

you need to do a little more plugging in

Answer 14

\(\sf b^2~=~12^2~+~19^2~-~2ac~cos105\)

Answer 15

Not quite
\(\large b^2=(12)^2+(19)^2-2(12)(19)\cos (105)\)

Answer 16

Oh whoops :/

Answer 17

:) Can you do the rest, or no?

Answer 18

I think so, I will let you know what I come up with if that is ok?

Answer 19

Okay,

Answer 20

I got approximately 25 for b

Answer 21

yes, although I prefer not to round too much until the very end, so I used 24.96 to plug in for the Heron's formula

Answer 22

Ok :)

Answer 23

Do you need help for the heron's part, or no...?

Answer 24

No, I had to find a notebook haha xD

Answer 25

okay, let me know what you get.

Answer 26

110.11

Answer 27

Perfect. Nice job. :)

Answer 28

yay! thank you :)

Answer 29

You're welcome. :)

Answer 30

There's no need to use the law of cosines since there is a shorter way
Look on this link where it says "Knowing Two Sides and the Included Angle"
http://www.mathsisfun.com/algebra/trig-area-triangle-without-right-angle.html

however, your method works just fine