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 show 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
B
C

Answer 1

135.5 m

Explanation:

Given a triangle with angles A=46°, B=103°, and side c=97 m, you want to find the length of side 'a'.

Law of Sines

Given one side and two angles we can solve the triangle using the Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

In order to do that, we need to have a (side, angle) pair, so we need to find the measure of angle C.

A + B + C = 180°

46° +103° +C = 180° . . . use the given measures

C = 31° . . . . . . . . . . . . . subtract 149°

Now, we can find 'a' from ...

a/sin(A) = c/sin(C)

a = c·sin(A)/sin(C) = (97 m)·sin(46°)/sin(31°) ≈ 135.477286 m

The distance from B to the tree at C is about 135.5 meters.