Question

One flies a kite with a thread 42 m long. If the thread of the kite makes an angle of 45° with the horizontal line, then the height of the kite from the ground is-

Answer 1

Given


The length of thread is 42m and the angle made by the thread is 45°

We have to calculate the height.

Since the height will be perpendicular to the ground, we can say the given figure is a right angled Triangle.


Now, Sin∅ = P/H

Where P = perpendicular and H = hypotenuse

Given H = 42m
Let P be h
and ∅ = 45°


=> sin45° = h/42

But sin45° = 1/√2

=> 1/√2 = h/42

Cross multiplication,

h√2 = 42

=> h =
$\frac{42}{ \sqrt{2} } \\ \\ = > \frac{42 \sqrt{2} }{ \sqrt{2 \times 2} } \\ \\ = > \frac{42 \sqrt{2} }{2} \\ \\ = > 21 \sqrt{2}$
So the height of the kite from the ground is 21√2 cm


Hope it helps dear friend ☺️

Answer 2

Given,

Length of thread =  42 m

Let that the person is  flying  kite upto point  C with 42 m long  thread which makes and  angle  of  45° from the ground as  shown in figure.The person is  standing  at  point  A.We  have  to find distance h.

Now,

In ΔABC,

sin45°=perpendicular/hypotenuse

$\sin45\textdegree=\frac{BC}{AC}\\\;\\\frac{1}{\sqrt{2}}=\frac{h}{\sqrt{42}}\\\;\\h=\frac{42}{\sqrt{2}}\\\;\\h=21\sqrt{2}\;m$