Question

Solve the triangle

Short answer

The solution is

$A=48.51°,B=38.62°,C=92.87°$

Step-by-step solution

Step1. Given information

Step2. Formula used

$$\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc}, \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}$$

Step3. Calculation

$$\begin{gathered} Weknow, \\ \cos A=\frac{b^2+c^2-a^2}{2bc} \\ =\frac{5^2+8^2-6^2}{2.5.8} \\ =\frac{25+64-36}{80} \\ =\frac{53}{80} \\ =.6625 \\ A={\cos }^{-1}\left(.6625\right) \\ =48.51° \\ Again, \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \\ =\frac{6^2+8^2-5^2}{2.6.8} \\ =\frac{36+64-25}{96} \\ =\frac{75}{96} \\ =.78125 \\ B={\cos }^{-1}\left(.78125\right) \\ =38.62° \\ Again,weknow \\ A+B+C=180° \\ 48.51°+38.62°+C=180° \\ C=180°-87.13° \\ =92.87° \end{gathered}$$