# How do you solve the triangle given r = 15, t = 8, angle S = 125º?

Jun 26, 2018

color(maroon)(s = 20.66, hat R = 36.49^@, hat T = 18.51^@

#### Explanation:

Law of cosines ${s}^{2} = {r}^{2} + {t}^{2} - 2 r t \cos S$

$r = 15 , t = 8 , \hat{S} = {125}^{\circ}$

${s}^{2} = {15}^{2} + {8}^{2} - \left(2 \cdot 15 \cdot 8 \cdot \cos \left(125\right)\right) = 426.66$

$s = \sqrt{426.66} \approx 20.66$

Law of Sines $\sin \frac{S}{s} = \sin \frac{R}{r} = \sin \frac{T}{t}$

$\sin R = \frac{r \sin S}{s} = \frac{15 \cdot \sin \left(125\right)}{20.66} = 0.5947$

$\hat{R} = {\sin}^{-} 1 \left(0.5947\right) = {36.49}^{\circ}$

$\hat{T} = 180 - 125 - 36.49 = {18.51}^{\circ}$