precalc math problem

Question

A pipeline is to be constructed between points A and B on opposite sides of a river, as shown in the figure. To determine the amount of pipe needed, using a theodolite at point A, a right triangle ACB is constructed with point C approximately 420 feet from A. At point A, the transit is used to determine that the angle F is 40°. Determine the amount of pipe needed to connect points A and B. (Round your answer to one decimal place.

Answer 1

angle A = 40 degrees

AC = 420 feet

ACB is a right triangle, find side CB

tan 40 = CB/AC

CB = 420tan40 ft = about 352.42 feet across the river