# Cos rule question

• Dec 19th 2010, 02:53 PM
jgv115
Cos rule question
I got this question, I know how to do it but the answer is never right

A weight is hung from two hooks in a ceiling by strings
of length 54 cm and 42 cm, which are inclined at 70◦ to
each other. Find the distance between the hooks.

$c^2 = 54^2+42^2 -(2)(54)(42) \cos 70$

Is this right?
• Dec 19th 2010, 02:55 PM
dwsmith
I believe it looks good.
• Dec 19th 2010, 07:29 PM
jgv115
Alright,

For this:http://i22.photobucket.com/albums/b3...Capture-10.png

It asks me to find CD. I've been trying ages but I have no idea how to do it. Can someone help me out?
• Dec 19th 2010, 07:57 PM
dwsmith
Use the law of cosine to solve BD.

$a^2=4^2+6^2-2*4*6*cos(92)\Rightarrow a=7.326=BD$

Now use the law of sine to solve the angle BDC.

$\displaystyle \frac{sin(88)}{7.326}=\frac{sin(BDC)}{5}\Rightarro w BDC=sin^{-1}\left(\frac{5sin(88)}{7.326}\right)=43.0043$

angle DBC = $180-88-43.0034=48.9957$

law of sine to solve DC

$\displaystyle \frac{sin(88)}{7.326}=\frac{sin(48.9956)}{DC}\Righ tarrow DC=\frac{7.326*sin(48.9957)}{sin(88)}=5.5323$
• Dec 19th 2010, 08:16 PM
jgv115
OMG!!! I'm so stupid!!!!

(sigh) I better keep practising these :(

Thanks a lot!