Solve the problem.
-Points A and B are on opposite sides of a lake. Point $C$ is $101.0$ meters from $A$. The measure of angle BAC is $76 ^ { \circ } 30 ^ { \prime }$, and the measure of angle ACB is determined to be $39 ^ { \circ } 30 ^ { \prime }$. Find the distance between points $\mathrm { A }$ and $\mathrm { B }$ (to the nearest meter).
A) $69 \mathrm {~m}$
B) $34 \mathrm {~m}$
C) $71 \mathrm {~m}$
D) $36 \mathrm {~m}$

Question

Quizplus · Accepted Answer

Using the Law of Sines, we can find the distance between points A and B. The sum of angles in a triangle is $180^\circ$, so angle $ABC = 180^\circ - 76^\circ 30' - 39^\circ 30' = 64^\circ$. Applying the Law of Sines: $\frac{AB}{\sin(39^\circ 30')} = \frac{101.0}{\sin(64^\circ)}$. Solving for $AB$ gives a distance of approximately $71$ meters.

Solve the Problem CCC Is 101.0101.0101.0 Meters From AAA the Measure of Angle BAC Is

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