# Thread: Cos rule question

1. ## 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?

2. I believe it looks good.

3. Alright,

For this:

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?

4. Use the law of cosine to solve BD.

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

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

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

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

law of sine to solve DC

$\displaystyle \displaystyle \frac{sin(88)}{7.326}=\frac{sin(48.9956)}{DC}\Righ tarrow DC=\frac{7.326*sin(48.9957)}{sin(88)}=5.5323$

5. OMG!!! I'm so stupid!!!!

(sigh) I better keep practising these

Thanks a lot!