# work out missing angle?

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• Dec 15th 2010, 07:03 AM
andyboy179
work out missing angle?
hi, i need to work out the angle in this shape:
Attachment 20114

im not really sure that to do but would this work:
cosA= 5^2 + 10^2 + 18^2/ 2x5x10= 449/100= 4.49?

is this correct? if not could you please tell me where im going wrong and what i need to do!?!

Thanks!
• Dec 15th 2010, 07:28 AM
Ackbeet
I don't think you're setting up your law of cosines correctly. Take a look at the wiki link, and tell me what the equation ought to be.
• Dec 15th 2010, 07:35 AM
andyboy179
one question, where would A,B and C be on my triangle?
• Dec 15th 2010, 07:37 AM
Ackbeet
Take a really good look at the wiki link. It explains how to assign all the variables in the equation there. Then you tell me how to assign them.
• Dec 15th 2010, 07:42 AM
andyboy179
would it be, ?^2= 7^2 + 5^2-2x7x5xcos38= 18.84, then square root it= 4.34?
• Dec 15th 2010, 07:44 AM
Ackbeet
Am I looking at the same picture you're looking at? I see a triangle with lengths 11, 18, and 10. You're asked to find the angle opposite the side of length 18. Is that correct?
• Dec 15th 2010, 07:47 AM
andyboy179
yes, would it be:
18^2= 7^2+5^2-2x5x7xcos?= ??
• Dec 15th 2010, 07:47 AM
Ackbeet
Where is the 7 and 5 coming from in your equation?
• Dec 15th 2010, 07:50 AM
andyboy179
GRRRR!!!! really sorry i was looking at the wrong question!

would it be:18^2= 10^2+11^2-2x10x11xcos?= ??
• Dec 15th 2010, 07:53 AM
Ackbeet
That looks better. Try solving for the cosine of the angle. What do you get?
• Dec 15th 2010, 07:57 AM
andyboy179
im not really sure how i would do that.
• Dec 15th 2010, 08:01 AM
Ackbeet
Well, if you need to, just substitute x = cos(?) and solve for x the way you would normally do in algebra. What do you get?
• Dec 15th 2010, 08:03 AM
andyboy179
i can't think im having a mental blank! grr!
• Dec 15th 2010, 08:10 AM
andyboy179
could you tell me how to do it please, i can't think!
• Dec 15th 2010, 08:21 AM
Ackbeet
Yes, you can think. Your equation is this:

$18^{2}= 10^{2}+11^{2}-2\times 10\times 11\times \cos(?)$

$324=100+121-220\cos(?)$
Your goal, as usual, is to get the $\cos(?)$ on one side of the equation and everything else on the other. What's your next step?