Solve.
-Points $\mathrm { A }$ and $\mathrm { B }$ are on opposite sides of a lake. A point $\mathrm { C }$ is $89.2$ meters from $\mathrm { A }$. The measure of angle BAC is $75 ^ { \circ } 40 ^ { \prime }$, and the measure of angle $\mathrm { ACB }$ is determined to be $39 ^ { \circ } 30 ^ { \prime }$. Find the distance between points $\mathrm { A }$ and $\mathrm { B }$ (to the nearest meter).
A) $30 \mathrm {~m}$
B) $61 \mathrm {~m}$
C) $32 \mathrm {~m}$
D) $63 \mathrm {~m}$

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° - 75°40' - 39°30' = 65°50'. Then, using the Law of Sines: (sin(75°40') / 89.2) = (sin(65°50') / AB). Solving for AB gives a distance of approximately 63 meters.

Solve -Points A\mathrm { A }A And B\mathrm { B }B Are on Opposite Sides of a Lake

Solve
-Points $\mathrm { A }$ And $\mathrm { B }$ Are on Opposite Sides of a Lake