Question

A tree 50m high broke at a point but did not separate the top of the tree touched the ground at a distance of 40m from its foot .find the height of the point from the ground at which the tree broke

Answer 1

Answer:

tree broke at 9m height from ground

Answer 2

The height of the point from the ground at which the tree broke is 9 m

Step-by-step explanation:

Refer the attached figure :

Height of tree = AB = 50 m

Let the height of the point from the ground at which the tree broke be x

So, CB = x

So, CD = AC = AB - CB = 50-x

The top of the tree touched the ground at a distance of 40m from its foot i.e. BD = 40 m

So, we will use Pythagoras theorem

$Hypotenuse^2=Perpendicular^2+base^2\\CD^2=CB^2+BD^2\\(50-x)^2=x^2+40^2\\2500+x^2-100x=x^2+1600\\900=100x\\9=x$

Hence the height of the point from the ground at which the tree broke is 9 m

#Learn more :

A tree 50m high broke at a point but did not separate the top of the tree touched the ground at a distance of 40m from its foot .find the height of the point from the ground at which the tree broke

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