A boat race runs along a triangular course marked by buoys A, B, and C. The race begins with the boats headed west for 3900 meters. The other two sides of the course
Lie to the north of the first side, and their lengths are 1900 meters and 2500 meters,
Respectively. Find the bearing for the last leg of the race. Round your answer to two
Decimals.
A) -inf°
B) 113.74°
C) 180.01°
D) 156.26°
E) 90.01°

Question

Quizplus · Accepted Answer

The last leg of the race forms the hypotenuse of a right-angled triangle, with the other two sides being 1900 meters and 2500 meters. Using trigonometry, specifically the tangent function, we can find the angle of the last leg relative to north. The angle θ can be found using tan(θ) = opposite/adjacent = 2500/1900. Solving for θ gives us the bearing from north. However, since the race starts heading west and the last leg is to the north of the first side, we need to adjust this angle to get the bearing from north. The correct bearing is found to be 113.74°, which accounts for the geometric and trigonometric calculations based on the given sides of the triangle.

A Boat Race Runs Along a Triangular Course Marked by Buoys