
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.
$\displaystyle c^2 = 54^2+42^2 (2)(54)(42) \cos 70 $
Is this right?


Alright,
For this:http://i22.photobucket.com/albums/b3...Capture10.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?

Use the law of cosine to solve BD.
$\displaystyle a^2=4^2+6^22*4*6*cos(92)\Rightarrow a=7.326=BD$
Now use the law of sine to solve the angle BDC.
$\displaystyle \displaystyle \frac{sin(88)}{7.326}=\frac{sin(BDC)}{5}\Rightarro w BDC=sin^{1}\left(\frac{5sin(88)}{7.326}\right)=43.0043$
angle DBC =$\displaystyle 1808843.0034=48.9957$
law of sine to solve DC
$\displaystyle \displaystyle \frac{sin(88)}{7.326}=\frac{sin(48.9956)}{DC}\Righ tarrow DC=\frac{7.326*sin(48.9957)}{sin(88)}=5.5323$

OMG!!! I'm so stupid!!!!
(sigh) I better keep practising these :(
Thanks a lot!