Answer
No such triangle exists because $A+B \gt 180$
Work Step by Step
Law of sines: $\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$
Here, $A=149^{\circ}; a=7; b=10$
From the given measurements and information it can be seen that we have two sides and one angle which corresponds to $SSA$ configuration.
$\dfrac{\sin 149}{7}=\dfrac{\sin B}{10} \implies B=\sin^{-1} (0.74) \approx 47.8$
Thus, no such triangle exists because $A+B \gt 180$
