Question

Points A and B are 150 m apart on one bank of a river. Point C is on the other bank of the river. The line of sight distance from A to C forms an angle and 28 degrees with the AB side of the river bank and the line of sight distance form B to C forms an angle of 56 degrees with the AB side of the river bank. How wide is the river?

Answer 1

You have ASA. Solve the triangle. (getting the two other sides, law of sines).

Now, area of the triangle= sqrt(s(s-a)(s-b)(s-c)) where s is the half-perimeter (this is known as Heron of Alexandria's formula).

Now set it equal to 1/2 Base*height,or
area= 1/2 (150)width river

setting the two areas equal, you can find the width of the river