Find how wide the river is

Question

I need to figure out how to solve this and write an essay on this:

 

A surveyor wants to find the width of a river without crossing it. He sights an abandoned tire on the opposite bank (the banks are straight and parallel) and measures the angle from where he stands relative to the shore to be 31 degrees. After walking precisely 15 feet away from the tire, he measures the angle to be 13.5 degrees. How wide is the river?

Answer 1

Let x = width of river

Let y = distance from top of bank to the tire

Let A = angle from edge of the opposite bank to the tire = 31 degrees

Let B = angle from 15 feet from the edge of the opposite bank to the tire = 13.5 degrees.

 

tan A = y/x;  y = x*tan A

tan B = y/(x+15) = x*tan A/(x+15)

tan B(x+15) = x*tan A

x*tan B + 15*tan B = x*tan A

15*tan B = x*tan A - x*tan B = x*(tan A - tan B)

x = 15*tan B/(tan A - tan B) = 15*0.2401/(0.6009 - 0.2401) = 9.98 feet

 

The river is 10 feet wide.

 

Answer 2

This is a bit hard to answer because your statement of the problem does not include a picture of precise description of the angles and distance.

 

Could you answer these questions so i can help you better?

 

1) Is the 31° angle measured from the bank the surveyor is standing on to the tire?

2) When he walks away from the tire, is he walking perpendicular to the river bank he is standing on?

 

When you provide the answers to these questions, I will be able to help you much better.