Solve the problem.
-To find the distance $\mathrm { AB }$ across a river, a distance $\mathrm { BC } = 658 \mathrm {~m}$ is laid off on one side of the river. It is found that $\mathrm { B } = 114.8 ^ { \circ }$ and $\mathrm { C } = 14.6 ^ { \circ }$. Find $\mathrm { AB }$ rounded to the nearest meter.
A) $218 \mathrm {~m}$
B) $215 \mathrm {~m}$
C) $166 \mathrm {~m}$
D) $169 \mathrm {~m}$

Question

Quizplus · Accepted Answer

Using the law of sines in triangle ABC, we find AB = BC * sin(C) / sin(A). With angles B = 114.8° and C = 14.6°, angle A = 180° - B - C = 50.6°. Thus, AB = 658 * sin(14.6°) / sin(50.6°) ≈ 215 m.

Solve the Problem AB\mathrm { AB }AB Across a River, a Distance

Solve the Problem $\mathrm { AB }$ Across a River, a Distance