.

[restive mantle]

That answer should be correct, by using sine's law.
for the area you can find angle ABC = 180-112-50 = 18.
Then use the sine area formula, which gives
$$\frac{5 \cdot |BC| \cdot \sin{18}^{\circ}}{2}$$

[rancid field]

Crystopher

[restive mantle]

you have found $|BC|$ in the previous part of the exercise.

[rancid field]

Crystopher