Question

Solve for 'x' csc∠A + tan∠C = 5x

Answer 1

You know that:
\[\csc(x)=\frac{\textrm{hypotenuse}}{\textrm{opposite}}\]
So:
\[\csc(A)=\frac{7}{6}\]
And tan(A)=opp/adj so opposite side for C is given by:
\[\sqrt{7^2-6^2}=\sqrt{13}\]
So:
\[\tan(C)=\frac{\sqrt{13}}{6}\]
\[5x=\frac{\sqrt{13}}{6}+\frac{7}{6}\]
Just divide by 5.