Question

A balloon’s thread

is 13m long and

reaches a window 12 m

above the ground. Find

the distance of the nail

to which balloon is tied

from base of the wall.​

Answer 1

Given:

A balloon’s thread   is 13m long and  reaches a window 12 m  above the ground

To find:

The distance of the nail  to which balloon is tied  from the base of the wall.​

Solution:

Let's assume,

AB = 12 m = the vertical distance between the window and the ground i.e., the perpendicular height

AC = 13 m = the length of the balloon's thread which is tied at the point C i.e., the hypotenuse

BC = the distance of the nail  to which balloon is tied  from the base of the wall i.e., the base

Now, considering Δ ABC, using the Pythagoras theorem, we get

$AC^2 = AB^2 + BC^2$

substituting the values of AB & AC, we get

$\implies 13^2 = 12^2 + BC^2$

$\implies BC^2 = 13^2 - 12^2$

$\implies BC = \sqrt{13^2 - 12^2}$

$\implies BC = \sqrt{169 - 144}$

$\implies BC = \sqrt{25}$

$\implies \bold{BC = 5\:m}$

Thus, the distance of the nail  to which balloon is tied  from the base of the wall is 5 m.

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