Solve.
-To find the distance AB across a river, a distance BC of 756 m is laid off on one side of the river. It is found that B = 109.4° and C = 13.9°. Find AB rounded to the nearest meter.
A) 220 m
B) 179 m
C) 182 m
D) 217 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 of 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. So, angle A = 180° - 109.4° - 13.9° = 56.7°. Now, applying the law of sines, we get (AB/sin(C)) = (BC/sin(A)). Plugging in the known values, (AB/sin(13.9°)) = (756/sin(56.7°)). Solving for AB gives AB ≈ 217 meters, rounded to the nearest meter.

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