# trig

posted by Ansley

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?

1. bobpursley

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

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