Answer
No triangle satisfies the conditions given.
Work Step by Step
$a=65$ $,$ $c=50$ $,$ $\angle C=52^{\circ}$
Find angle $A$ by using the formula $\dfrac{\sin A}{a}=\dfrac{\sin C}{c}$, obtained from the Law of Sines. Substitute the known values and solve for $A$:
$\dfrac{\sin A}{65}=\dfrac{\sin52^{\circ}}{50}$
$\sin A=\Big(\dfrac{65}{50}\Big)\sin52^{\circ}$
$\sin A=\Big(\dfrac{13}{10}\Big)\sin52^{\circ}$
$A=\sin^{-1}\Big[\Big(\dfrac{13}{10}\Big)\sin52^{\circ}\Big]$
Since $\dfrac{13}{10}\sin52^{\circ}\approx1.0244$ and the sine is never greater than $1$, then no triangle satisfies the conditions given.
