Answer
$$219 \space ft$$
Work Step by Step
$$\angle A + \angle B + \angle C = 180^o$$ $$82^o + 52^o + \angle C= 180^o$$ $$\angle C = 180^o -82^o - 52^o = 46^o$$
The distance from A to C is represented by $b$ on the drawing. Therefore, we can use the law of sines to calculate its value:
$$\frac{sin \space B}{b} = \frac{sin \space C} c$$ $$c \space sin \space B = b \space sin \space C$$ $$c \space \frac{sin \space B}{sin \space C} = b$$ $$b = c \space \frac{sin \space B}{sin \space C} = (200 \space ft) \frac{sin \space 52^o}{sin \space 46^o} = 219 \space ft$$
