A vertical tree is broken by the wind at a height of 6m from its foot and its top touches
the ground at a distance of 8 cm from the foot of tree. Calculate the distance between
the top of the tree before breaking and the point at which the tree touches the ground
after break
Answers
Let x be the length of broken part.
Let x be the length of broken part.Total height of tree-x+6 m
Let x be the length of broken part.Total height of tree-x+6 mDistance between foot of tree and the point where the tree touch the ground=8 m
Let x be the length of broken part.Total height of tree-x+6 mDistance between foot of tree and the point where the tree touch the ground=8 mIn triangle BCD
BD²BC²CD²
Using Pythagoras theorem
(Hypotenuse)² = (Base)² +
(Perpendicular side)2
2²628²36+64=100
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Answer:
Let x be the length of broken part.
Total height of tree =x+6 m
Distance between foot of tree and the point where the tree touch the ground =8 m
In triangle BCD
BD
2
=BC
2
+CD
2
Using Pythagoras theorem
(Hypotenuse)
2
=(Base)
2
+(Perpendicularside)
2
x
2
=6
2
+8
2
=36+64=100
x=
100
=10 m
Total height of tree =x+6=10+6=16 m
In triangle ACD
AD
2
=AC
2
+CD
2
Substitute the values
AD
2
=(16)
2
+8
2
AD
2
=256+64
AD
2
=320
AD=
320
=8
5
m
Hence, the distance between the top and the point where the tree touches the ground =8