Maths-
General
Easy
Question
A tree 90 m high broke at a point but did not separate. Its top touched the ground at a distance of 27 m from its base. Find the height of the point from the ground, at which the tree broke?
The correct answer is: Hence, the height of the point from the ground, at which the tree broke is 40.95 m
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
Solution
Let the height of the point from the ground, at which the tree broke be x m. So, the diagram representing the given condition is as
Applying Pythagoras theorem in △ABC
BC2 = AB2 + AC2
(90 - x)2 = x2 + 272
8100 + x2 - 180x = x2 + 729
180 x = 7371
x = 40.95 m
Final Answer:
Hence, the height of the point from the ground, at which the tree broke is 40.95 m
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