Swaraj observed two men standing on top of two hills on the bank of pond,of heights 250 m and 522 m,on opposite sides of the pond and measuring the angles of depression of a toy floating on the water at 45 0 and 60 0 respectively. The depth of the pond is 14 m. What will be the distance between the two men.(assume here the width of the hills and height of the persons are negligible and use root 3 = 1.73)
Answers
Given : two men standing on top of two hills on the bank of pond,of heights 250 m and 522 m,on opposite sides of the pond and measuring the angles of depression of a toy floating on the water at 45° and 60° respectively
To find : distance between the two men.
Solution:
Horizontal Distance of toy from 250 m hill = a
angles of depression of a toy floating on the water 45°
=> tan 45° = 250/a
=> 1 = 250/a
=> a = 250
Horizontal Distance of toy from 522 m hill = b
angles of depression of a toy floating on the water 60°
=> tan 60° = 522/b
=>√3 = 522/b
=> b = 301.7 m
Width of pond = 250 + 301.7 = 551.7 m
vertical Distance between two men = 522 - 250 = 272 m
Distance between two men = √( 551.7)² + (272)²
= 615.1 m
distance between the two men. = 615.1 m
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