Question

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60^. When he retreats 20 feet from the bank, he finds the angle to be 30^. The breadth of the river in feet is:

• A. 15
• B. 15√(3)
• C. 10√(3)
• D. 10

Hint:

Use tangent ratios for angles of elevation.

Answer 1

The Correct Option is C

Let the width of the river be x. From first position: 60^=(h)/(x) h=√(3)x From second position: 30^=(h)/(x+20)=1√(3) h=x+20√(3) Equating values of h: √(3)x=x+20√(3) 3x=x+20 x=10 Thus breadth =10√(3) ft.