An engineer wants to construct a bridge across a fast moving river. Using a straight line segment between two points that are 95 feet apart along his side of the river, he measures the angles formed when sighting the point on the other side where he wants to have the bridge end. If the angles formed at points A and B are 78° and 37°, respectively, how far is it from point A to the point on the other side of the river? Round to one decimal place.
A) 63.1 feet
B) 102.5 feet
C) 143.1 feet
D) no solution

Question

Quizplus · Accepted Answer

The correct answer is A because the distance from point A to the point on the other side of the river is 63.1 feet. This can be found using the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle. In this case, we have:AB/sin(78°) = BC/sin(37°)Solving for BC, we get:BC = AB * sin(37°) / sin(78°)Substituting AB = 95 feet, we get:BC = 95 feet * sin(37°) / sin(78°)BC = 63.1 feet (rounded to one decimal place)

An Engineer Wants to Construct a Bridge Across a Fast