Question

To find the distance from the edge of a lake to the tree on the island in the lake, Lisa sets up a triangular configuration as shown in the diagram. The distance from Location A to Location B is 97 meters. The measures of the angles at A and B are 46° and 103°. What is the distance from the edge of the lake at B to the tree on the island at C? Round the distance to the nearest tenth of a meter.

A. 120.6 meters
B. 135.5 meters
C. 140.8 meters
D. 160.1 meters

Answer 1

To find the distance from the edge of the lake at B to the tree on the island at C, use the Law of Sines. The distance is B) 135.5 meters.

Step-by-step explanation:

To find the distance from the edge of the lake at B to the tree on the island at C, we can use the Law of Sines.

First, let's label the angles of the triangle: angle A is 46°, angle B is 103°, and angle C is 180° - 46° - 103° = 31°.

We know the length of side AB is 97 meters.

Using the Law of Sines, we can set up the equation: (BC/sin(46°)) = (AB/sin(31°)). Solving for BC, we get BC = AB * (sin(46°)/sin(31°)).

Plugging in the values, BC = 97 * (sin(46°)/sin(31°)) = 135.5 meters.

Therefore, the distance from the edge of the lake at B to the tree on the island at C is approximately 135.5 meters.