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 :

Step-by-step solution

et (h ) be the height of tree PQ and breadth of river PS be (x ~ft ). Angle of elevation subtended by a tree is (60^ ). Also, when he retreats 20 feet, the angle becomes (30^ ). Also, in ( PQS ), ( aligned & 60^ = h x & h= 3 x aligned ) and in ( PQR ), ( aligned & 30^ = h x+20 1 3 = h x+20 & x+20= 3 h & x+20=3 x 2 x=20 x=10 aligned ) Hence breadth of river is (10 ft ).