Solve.
-To find the distance $\mathrm { AB }$ across a river, a distance $\mathrm { BC }$ of $786 \mathrm {~m}$ is laid off on one side of the river. It is found that $\mathrm { B }$ $= 110.2 ^ { \circ }$ and $\mathrm { C } = 13.5 ^ { \circ }$. Find $\mathrm { AB }$.
A) $224 \mathrm {~m}$
B) $221 \mathrm {~m}$
C) $182 \mathrm {~m}$
D) $185 \mathrm {~m}$

Question

Quizplus · Accepted Answer

Using the law of sines in triangle ABC, we have $\frac{AB}{\sin C} = \frac{BC}{\sin A}$. Given $\angle B = 110.2^\circ$ and $\angle C = 13.5^\circ$, $\angle A = 180^\circ - 110.2^\circ - 13.5^\circ = 56.3^\circ$. Thus, $AB = \frac{786 \sin 13.5^\circ}{\sin 56.3^\circ} \approx 221 \mathrm{~m}$.

Solve -To Find the Distance AB\mathrm { AB }AB Across a River, a Distance

Solve
-To Find the Distance $\mathrm { AB }$ Across a River, a Distance