104.5 degree triangle w/ 2 equal legs, need the 3rd leg's length

AI Thread Summary
To find the length of the third leg of a triangle with two equal legs of 96 inches and an included angle of 104.5 degrees, the Law of Cosines is applicable. The equation used is C^2 = A^2 + B^2 - 2AB*cos(θ), where A and B are the lengths of the legs, and θ is the included angle. A user initially struggled with the calculation, obtaining an incorrect result of 1.17545571 instead of the expected 1.5. It was identified that a mistake was made by omitting a minus sign in the cosine calculation. Correcting this error allowed for a better understanding of the Law of Cosines and yielded the correct length for the third leg.
CocoonOHorror
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Homework Statement



i have a triangle with 2 legs of 96 inches. the angle between them is 104.5 degrees. how do i get the length of the 3rd leg?

Homework Equations

wish i knew.


The Attempt at a Solution


tried Cos, Sin, and Tan of 104.5 * length of a leg
 
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Draw a line down the centre. Now you have two right-angled triangles. It should be a piece of cake from there.
 
willem2 said:
How about the cosine rule?

http://en.wikipedia.org/wiki/Law_of_cosines

works for unequal legs as well.

when i tried this i got 1.17545571, but the answer should be 1.5.

C^2=(.96)^2+(.96)^2-2(.96)(.96)(-.25038)
 
DaveC426913 said:
Draw a line down the centre. Now you have two right-angled triangles. It should be a piece of cake from there.

thanks man! i think this worked, and i kind of understand why.

i still don't understand why the law of cosines didnt work for me, i wonder what i screwed up...
 
CocoonOHorror said:
when i tried this i got 1.17545571, but the answer should be 1.5.

C^2=(.96)^2+(.96)^2-2(.96)(.96)(-.25038)

you forgot one of the minus signs in -2(.96)(.96)(-.25038)
 
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