The tip of a plant was 6cm above a lake but a sudden wind forced the plant to move 10 cm fat from its original position and then it submerged into the lake. Find the depth of the lake upto which it was sinking.
Please help!!!!!!!!!!
Make a sketch.
Think of the plant as a radius of a circle the plant would draw out.
Draw in a horizontal to show the lake.
At the vertical let OP be the length of the plant,
O is the centre and P at the top.
then draw a horizontal 6 cm below P so the plant touches at A and B.
OP = x , AP = 6 , AB = 10, and OB = x
then OA = x-6
by Pythagoras,
x^2 = 10^2 + (x-6)^2
x^2 = 100 + x^2 - 12x + 36
12x = 136
x = 136/12 = 34/3 or 11 1/3
then the depth of the plant below water
= 34/3 - 6
= 16/3 or
5 1/3 cm