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Law of Cosines Problem Help

I need help with this problem [url=http://i.imgur.com/z4NU8Lh.png]here[/url] . I used c^2=a^2+b^2 - 2(a)(c)CosC and I ended up with 576 = 841 + b^2 - 58(b)CosC.

EDIT: I know that the answer is 35 degrees (100% sure), but I need to know how to get there. I'm using c^2=a^2+b^2 - 2(a)(b) made a typo in first equation. Still no understanding of how to get 35 degrees for my answer.

February 14, 2013

12 Comments • Newest first

Al3xL3g3nd

[quote=alex3650]Thank you guys for all of the help !
@Al3xL3g3nd What do you do if you do Cos101 on a calculator and get a negative number?[/quote]
It's because cosine is negative from 90 deg to 180 deg in a circle.
I put the equation in wolfram alpha and it came out with a positive number for c.

Reply February 14, 2013 - edited
JaydenVo

Set your equation to equal b. [b^2=a^2+c^2 - 2(a)(c)cosB]
b^2 = 29^2 + 24^2 - 2(29)(24)cos(101)
Put [29^2 + 24^2 - 2(29)(24)cos(101)] into your calculator to get
b^2 = 1682.606122
Square root this number to get b

Now that you have side b, you can complete your C equation. [c^2=a^2+b^2 - 2(a)(b)cosC]
(I'll write b as the variable cause it's an ugly number lol)
24^2=29^2+b^2 - 2(29)(b)cosC
24^2=576
Find [29^2+b^2] from the calculator. We'll call it X.
Then find [-2(29)(b)] This will be Y. We're just combining like terms to make the algebra easy.

579 = X + YcosC
Subtract X from both sides. (This usually leaves both sides of the equation negative.)
Now divide both sides by Y. (Y is negative most of the time.)
Find the inverse cos of that answer, and you've got yourself C.

Edit: @alex3650 that number will be multiplied with another negative, making it a positive.

Reply February 14, 2013 - edited
alex3650

Thank you guys for all of the help !
@Al3xL3g3nd @JaydenVo What do you do if you do Cos101 on a calculator and get a negative number?

Reply February 14, 2013 - edited
bloodIsShed

first, apply the law to find b:
b^2 = 29^2 + 24^2 - 2*29*24cos(101)

then apply the formula again to find cos C
24^2 = 29^2 + b^2 - 29*b cos C

then use the calculator to find the inverse cosine C to get the angle

edit: ninja'ed

Reply February 14, 2013 - edited
Al3xL3g3nd

Using CB as a and BA as b and <B as C

c^2=29^2+24^2-2(29)(24)cos101 (remember to be in degree mode when using your calc since we are in degrees)
c=41.02

Now that you have the length of another side you can use law of cosines again
Using BA as c and CB as a and CA as b

24^2=29^2+41.02^2-2(29)(41.02)cosc

Do the algebra to get your answer.

Reply February 14, 2013 - edited
alex3650

[quote=JaydenVo]@alex3650: Well, I had to find b before I could find C
I got the answer, if you need some help btw.[/quote]
Step by step help would be nice, thank you !

Reply February 14, 2013 - edited
JaydenVo

@alex3650: Well, I had to find b before I could find C
I got the answer, if you need some help btw.

Reply February 14, 2013 - edited
alex3650

[quote=JaydenVo]I just tried finding angle C, and there was no side c. I think you meant to find side b, right?[/quote]

No, it's find <C
@bloodIsShed Can you help me solve by steps? Thanks

Reply February 14, 2013 - edited
JaydenVo

I just tried finding angle C, and there was no side c. I think you meant to find side b, right?

Reply February 14, 2013 - edited
alex3650

[quote=DarkRecon]c^2=a^2+b^2 - 2(a)([b]b[/b])CosC

see if that fixes things[/quote]

Ohh.. thanks made a typo

Reply February 14, 2013 - edited
bloodIsShed

he just made a typo.
at TS: you're supposed to use the given angle (101)

edit to avoid possible confusion: rewrite the expression, but use the angle already given, instead of picking an unknown angle

Reply February 14, 2013 - edited
DarkRecon

c^2=a^2+b^2 - 2(a)([b]b[/b])CosC

see if that fixes things

Reply February 14, 2013 - edited