# Thread: Sloving triangle with law of sine and cosine

1. ## Sloving triangle with law of sine and cosine

Solve the missing angles
a=15cm b=18cm c=30cm
so If I use $\displaystyle a^2=b^2+c^2-2bc\cdot\cos A$
i get angle A is 42.12 degrees but then B and C don't work out i know I can use the law of sine once I have one angle but I am just asking why doesn't B and C work with the law of cosine?

2. ## Re: Sloving triangle with law of sine and cosine

$\displaystyle \cos{A} = \frac{b^2+c^2-a^2}{2bc}$

$\displaystyle \cos{B} = \frac{a^2+c^2-b^2}{2ac}$

$\displaystyle \cos{C} = \frac{a^2+b^2-c^2}{2ab}$

3. ## Re: Sloving triangle with law of sine and cosine

Originally Posted by skeeter
$\displaystyle \cos{A} = \frac{b^2+c^2-a^2}{2bc}$

$\displaystyle \cos{B} = \frac{a^2+c^2-b^2}{2ac}$

$\displaystyle \cos{C} = \frac{a^2+b^2-c^2}{2ab}$

Skeeter when I Calculated it for cos B $\displaystyle \frac{325-225+900}{900} = \frac{999}{900} =1.11$
and then but my answer should be between 0 and 1 and this doesn't work why?
I see my mistake I think

4. ## Re: Sloving triangle with law of sine and cosine

look at the signs in the numerator ...

5. ## Re: Sloving triangle with law of sine and cosine

Originally Posted by M670
Skeeter when I Calculated it for cos B $\displaystyle \frac{325-225+900}{900} = \frac{999}{900} =1.11$
and then but my answer should be between 0 and 1 and this doesn't work why?
I see my mistake I think
Its -324+225+900/900 =.81 not 1.11

6. ## Re: Sloving triangle with law of sine and cosine

It helps to construct a triangle of 1/2 size but label sides as given

For the obtuse angle cos A = (15^2 + 18^2 - 30^2) / 2*15*18 =-0.65
A= 130.5

7. ## Re: Sloving triangle with law of sine and cosine

Its -324+225+900/900 =.81 not 1.11www.louisvuittonend.com