Law of cosines:
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
For the given triangle:
[tex]\begin{gathered} a=26 \\ b=50 \\ c=29 \\ A=x \\ \\ a^2=b^2+c^2-2bc\cos A \end{gathered}[/tex][tex]26^2=50^2+29^2-2(50)(29)\cos x[/tex]
Solve x from the equation above:
[tex]\begin{gathered} 676=2500+841-2900\cos x \\ 676=3341-2900\cos x \\ 676-3341=-2900\cos x \\ -2665=-2900\cos x \\ \frac{-2665}{-2900}=\cos x \\ \\ \cos x=\frac{533}{580} \\ \\ x=\cos^{-1}(\frac{533}{580}) \\ \\ x\approx23.2 \end{gathered}[/tex]Then, the value of x is 23.2º
