To find the distance across a river a surveyor chooses point

To find the distance across a river, a surveyor chooses points A and B, which are x = 300 ft apart on one side of the river (see the figure). She then chooses a reference point C on the opposite side of the river and finds that angle BAC = 82degree and angle ABC = 52degree. Approximate the distance from A to C. (Round your answer to the nearest foot.)

Solution

First find angle ACB = 180 -52 -82 = 46 deg

Applying sine rule:

AC/sin52 = 300/sin46

AC = sin52*300/sin46 = 328.63 = 329 foot