# In triangle KLM, if k=4, l=5, m=8, how do you find the exact value of cos M?

Nov 8, 2017

$\cos M = - \frac{23}{40}$

#### Explanation:

we need tot use the cosine rule

${a}^{2} = {b}^{2} + {c}^{c} - 2 b \mathcal{o} s A$

we are given

$k = 4 , l = 5 , m = 8$

we have to find $\cos M$

so the cosine rule for this problem becomes

${m}^{2} = {k}^{2} + {l}^{2} - 2 k l \cos M$

$\therefore {8}^{2} = {4}^{2} + {5}^{2} - 2 \times 4 \times 5 \cos M$

$64 = 41 - 40 \cos M$

rearranging for $\cos M$

$\frac{64 - 41}{- 40} = \cos M$

$\cos M = - \frac{23}{40}$