# The lengths of side b is 15cm, c is 24cm and a is 18cm. How do you calculate the angle B (which is opposite side b)?

Dec 13, 2016

${38.62}^{\circ}$

#### Explanation:

Use the law of cosine of solving triangles :

${b}^{2} = {a}^{2} + {c}^{2} - 2 \cdot a \cdot c \cdot \cos B$

$\implies {15}^{2} = {18}^{2} + {24}^{2} - 2 \cdot 18 \cdot 24 \cdot \cos B$

$\implies C o s B = \frac{{18}^{2} + {24}^{2} - {15}^{2}}{2 \cdot 18 \cdot 24} = 0.78125$

$\implies B = {\cos}^{-} 1 \left(0.78125\right) = {38.62}^{\circ}$ (two decimal place)