To find the distance across a river a surveyor chooses points $A$ and $B$, $50$M apart and a reference point $C$On the opposite side of theriver. Approximate the distance, $b$, between $A$ And $C$Given that $\angle \mathrm { A } =54 ^ { \circ }$And $\angle B = 77 ^ { \circ }$
A) $54.6 \mathrm {~m}$
B) $77.6 \mathrm {~m}$
C) $64.6 \mathrm {~m}$
D) $45.6 \mathrm {~m}$
E) $85.6 \mathrm {~m}$

Question

Quizplus · Accepted Answer

We can use the law of sines to solve for $b$. Let $x$ be the distance between point $C$ and the intersection point of the line connecting $A$ and $B$ with the perpendicular bisector to the segment $AB$. Then, we have:

$$\frac{\sin(54^\circ)}{50}=\frac{\sin(77^\circ)}{b}=\frac{\sin(49^\circ)}{x}$$

Solving for $b$, we get:

$$b=\frac{\sin(77^\circ)}{\sin(54^\circ)}\cdot50\approx64.6\mathrm{~m}$$

Therefore, the answer is choice C.

To Find the Distance Across a River a Surveyor Chooses AAA

To Find the Distance Across a River a Surveyor Chooses $A$