# The Cosine Rule

• Mar 30th 2008, 01:40 AM
Stevo_Evo_22
The Cosine Rule
Hi guys,

I have a question on the cosine rule that i think i am getting right but the books answers tell me that its wrong. Its really easy:

In triangle ABC, a=8cm, b=10cm, C(Angle)=56.2 degrees. Find c(missing side).

Thanks in advance (im sure im right):)

Steve
• Mar 30th 2008, 01:47 AM
well it isnt that difficult o.o" books aren't perfect xD

C^2 = A^2 + B^2 - 2AB Cos(c)
C^2 = 8^2 + 10^2 - 2(8)(10) Cos (56.2)
C = 8.65983265
• Mar 30th 2008, 01:53 AM
Stevo_Evo_22
Thanx heaps, but thats exactly what i did and i keep ending up with around 14.

So i got:

a^2=100 + 64 -(-52.8)
a^2=164+52.8
a=14.724......
• Mar 30th 2008, 02:03 AM
i think you got the triangle wrong o.o"

you got the 100 and 64 correctly but your last term i don't understand how you get it

try :
Cosine Rule
• Mar 30th 2008, 02:07 AM
Stevo_Evo_22
I did:

2x8x10xcosx56.2
• Mar 30th 2008, 02:11 AM
If you are using a calculator calculate the value for cos 56.2 (in degree) first before you multiply it with 2, 8 and 10

well if you still don't get

cos 56.2 = 0.556295615

then it is time you change a new calculator o.o" i tried on two of mine and they obtained the same value
• Mar 30th 2008, 02:15 AM
Stevo_Evo_22
Ok so i get 89.007298......and i add it to 164 and get 253.007....and then i square-root it and get 15.906.....
• Mar 30th 2008, 02:18 AM
you need to minus 89.007298 from 164 not adding them up.

C^2 = A^2 + B^2 - 2A(B)cos (c)
= 164 - 89.007298
= 74.99270152

C = sqrt(74.99270152)
= 8.65983265
• Mar 30th 2008, 02:22 AM
Stevo_Evo_22
wow thankyou so much, it makes sense but why do you have to multiply cos first?
• Mar 30th 2008, 02:28 AM
Stevo_Evo_22
Oh its ok i got the answer now. I kept getting 14 but it was around 8
• Mar 30th 2008, 02:31 AM