Answer
$161.07$ft
Work Step by Step
Apply law of sines formula.
$\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$
or, $\sin C=\dfrac{165 \sin 67^{\circ}}{180}=0.844$
This gives: $C=57.54^{\circ}$ or, $C=122.46^{\circ}$
But, $122.46^{\circ}+67^{\circ} \gt 180^{\circ}$ , so we will have the value of $C$ is: $C=57.54^{\circ}$
Now, we have $A=180^{\circ}-B-C=55.46^{\circ}$
$\dfrac{\sin 55.46^{\circ}}{a}=\dfrac{\sin 67^{\circ}}{b}$
or, $a=\dfrac{180 \sin 67^{\circ}}{\sin 55.46^{\circ}}=161.07$ft
