vertical pole which is 2.25m long casts a 6.75m long shadow on the ground. at the same time a vertical tower casts a 90m long shadow on the ground. find the height of the tower.
Answers
Step-by-step explanation:
Given :-
A vertical pole which is 2.25m long casts a 6.75m long shadow on the ground. At the same time a vertical tower casts a 90m long shadow on the ground.
To find :-
Find the height of the tower. ?
Solution :-
Given that
Height of the pole = 2.25 m
Length of its shadow = 6.75 m
Let the height of the tower be h m
The length of its shadow = 90 m
This is the daily life situation which is application of Similar triangles
Convert the given data into pictorial representation then
In ∆ ABC , AB = 2.25 m and BC = 6.75 m
I'm ∆ DEF, FD = h m and DE = 90 m
We know that
The ratio of the corresponding sides are equal in two similar triangles
=> AB / BC = FD / DE = AC / FE
=> 2.25 / 6.75 = h / 90
=> (225/100) / (675/100) = h / 90
=> 225/675 = h / 90
=> (1×225) / (3×225) = h / 90
=> 1 / 3 = h / 90
On applying cross multiplication then
=> 3×h = 1×90
=> 3h = 90
=> h = 90/3
=> h = 30 m
Therefore, height = 30 m
Answer:-
The height of the tower for the given problem is 30 m
Used formulae:-
If two triangles are said to be similar,
- The corresponding angles are equal.
- The corresponding sides are in the same ratio ( in Proportion).
