Question

Solve the triangle

Short answer

The solution is$A=67.98°,B=44.04°,C=67.98°$

Step-by-step solution

Step2. Given information

$Here,a=4,b=3,c=4$

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

We know

$$\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc} \\ =\frac{3^2+4^2-4^2}{2.3.4} \\ =\frac{9+16-16}{24} \\ =\frac{9}{24} \\ =.375 \\ A={\cos }^{-1}\left(.375\right) \\ =67.98° \\ Again, \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \\ =\frac{4^2+4^2-3^2}{2.4.4} \\ =\frac{16+16-9}{32} \\ =\frac{23}{32} \\ =.71875 \\ B={\cos }^{-1}\left(.71875\right) \\ =44.04° \\ Weknow, \\ A+B+C=180° \\ 67.98°+44.04°+C=180° \\ C=180°-112.02 \\ =67.98° \end{gathered}$$