Solve the problem.
-Points A and B are on opposite sides of a lake. Point C is $99.6$ meters from A. The measure of angle $\mathrm { BAC }$ is $77 ^ { \circ } 50 ^ { \prime }$, and the measure of angle $\mathrm { ACB }$ is determined to be $33 ^ { \circ } 50 ^ { \prime }$. Find the distance between points $A$ and $B$ (to the nearest meter).
A) $58 \mathrm {~m}$
B) $30 \mathrm {~m}$
C) $60 \mathrm {~m}$
D) $28 \mathrm {~m}$

Question

Quizplus · Accepted Answer

To find the distance between points A and B, we can use the Law of Sines in triangle ABC. First, we find the measure of angle ABC by subtracting the given angles from 180° (since the sum of angles in a triangle is 180°). Angle ABC = 180° - 77°50' - 33°50' = 68°20'. Then, using the Law of Sines: $\frac{AB}{\sin(33°50')} = \frac{99.6}{\sin(68°20')}$. Solving for AB gives a distance of approximately 60 meters.

Solve the Problem 99.699.699.6 Meters from A BAC\mathrm { BAC }BAC Is 77∘50′77 ^ { \circ } 50 ^ { \prime }77∘50′

Solve the Problem $99.6$ Meters from A $\mathrm { BAC }$ Is $77 ^ { \circ } 50 ^ { \prime }$