Solve Applied Problems Using the Law of Sines
-To find the distance $\mathrm { AB }$ across a river, a distance $\mathrm { BC }$ of $293 \mathrm {~m}$ is laid off on one side of the river. It is found that $\mathrm { B } = 110.8 ^ { \circ }$ and $\mathrm { C } = 17.9 ^ { \circ }$. Find $\mathrm { AB }$. Round to the nearest meter.
A) 115 meters
B) 118 meters
C) 90 meters
D) 87 meters

Question

Quizplus · Accepted Answer

Explanation:Using the Law of Sines, we have:$$\frac{AB}{\sin C} = \frac{BC}{\sin B}$$Substituting the given values, we get:$$\frac{AB}{\sin 17.9^\circ} = \frac{293 	ext{ m}}{\sin 110.8^\circ}$$Solving for AB, we get:$$AB = \frac{293 	ext{ m} 	imes \sin 17.9^\circ}{\sin 110.8^\circ} \approx 118 	ext{ m}$$Therefore, the distance AB across the river is approximately 118 meters.

Solve Applied Problems Using the Law of Sines -To Find AB\mathrm { AB }AB

Solve Applied Problems Using the Law of Sines
-To Find $\mathrm { AB }$