Solve the problem.
-To find the distance AB across a river, a distance BC = 346 m is laid off on one side of the river. It is found that B = 115.1° and C = 13.6°. Find AB rounded to the nearest meter.
A)107 m
B)80 m
C)104 m
D)83 m

Question

Quizplus · Accepted Answer

Using the law of sines, we can find the distance AB across the river. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles in the triangle. In triangle ABC, we have side BC and angles B and C. We can find angle A using the fact that the sum of angles in a triangle is 180 degrees: A = 180° - B - C = 180° - 115.1° - 13.6° = 51.3°. Then, using the law of sines: AB/sin(C) = BC/sin(A), or AB = BC*sin(C)/sin(A) = 346*sin(13.6°)/sin(51.3°) ≈ 104 meters, rounded to the nearest meter.

Solve the Problem. -To Find the Distance AB Across a River, a Distance