# How do you solve for Angles A, B, C if a=20 b=30 c=25?

Mar 20, 2018

$C \approx {55.77}^{\circ} , B \approx {82.82}^{\circ} , \mathmr{and} , A \approx {41.41}^{\circ}$.

#### Explanation:

By the cosine formula, we have,

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

$= \frac{{30}^{2} + {25}^{2} - {20}^{2}}{2 \cdot 30 \cdot 25}$,

$= \frac{1125}{1500}$.

$\Rightarrow \cos A = 0.75$.

$\therefore A = a r c \cos 0.75 \approx {41.41}^{\circ}$.

$B = a r c \cos \left(\frac{{c}^{2} + {a}^{2} - {b}^{2}}{2 c a}\right)$,

$= a r c \cos \left(\frac{625 + 400 - 900}{2 \cdot 25 \cdot 20}\right)$

$= a r c \cos \left(0.125\right)$.

$\therefore B \approx 82.82$.

Finally, $C \approx {180}^{\circ} - \left({41.41}^{\circ} + {82.82}^{2}\right) = {55.77}^{\circ}$.