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Kareem and Amy are standing on a riverbank, $$150$$ meters apart, at points $$A$$ and $$B$$ respectively. (See the figure below.) They want to know the distance from Kareem to a house located across the river at point $$C$$ . Kareem measures angle $$A$$ (angle $$B A C$$ ) to be $$55 ^ { \circ }$$ , and Amy measures angle $$B$$ (angle $$A B C$$ ) to be $$74 ^ { \circ }$$ . What is the distance from Kareem to the house? Round your answer to the nearest tenth of a meter.
$$\angle C= 180- 55- 74= 51\\ \frac { \sin 51} { 150} = \frac { \sin 74} { d} \\ d= 185.5$$