A man sitting at a height of 20m on a tall tree on a small island in the middle of a river observes 2 poles directly opposite to each other on the 2 banks of the river and in line with a foot of tree. If the angles of depression of the feet the pole from a point at which the man is sitting on the tree on either side of the river are 60 degrees and 30 degrees respectively. Find the width of the river.

Asked by dr.geetanjali.p | 2nd Sep, 2019, 11:37: AM

Expert Answer:

XO rightwards arrow tree
Poles space at space straight Y space and space straight Z
YZ rightwards arrow width space of space river
In increment XOY
tan space 30 equals 20 over YO
YO equals 20 square root of 3 straight m
In increment XZO
tan space 60 equals 20 over ZO
ZO equals fraction numerator 20 over denominator square root of 3 end fraction straight m
YZ equals 20 square root of 3 plus fraction numerator 20 over denominator square root of 3 end fraction
equals fraction numerator 60 plus 20 over denominator square root of 3 end fraction
equals fraction numerator 80 square root of 3 over denominator 3 end fraction straight m

Answered by Arun | 2nd Sep, 2019, 04:46: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.