Question

A kite is flying with a thread of 150meters lenghth from a feild. If the thread of kite makes an angle 60° with the horizontal line, let us write by calculating the height of the kite from the ground.​

Answer 1

✬ Height = 75√3 m ✬

Step-by-step explanation:

Given:

• Length of thread of kite is 150 metres.
• Thread of kite makes an angle of 60°.

To Find:

• What is the height of kite from ground?

Solution: Let AB be the height of kite, AC be the length of thread and angle of elevation formed by kite is ∠ACB.

➟ CB is the horizontal line so height will be perpendicular i.e ∠ABC = 90°

Now, in right angled triangle ABC,

$\implies{\rm }$ sin θ = Perpendicular/Hypotenuse

$\implies{\rm }$ sin C = AB/AC

$\implies{\rm }$ sin 60° = AB/150

$\implies{\rm }$ √3/2 = AB/150

$\implies{\rm }$ 150√3 = 2AB

$\implies{\rm }$ 150√3/2 = AB

$\implies{\rm }$ 75√3 = AB

Hence, the height of kite from ground is 75√3 m.

Answer 2

$\huge\underline\mathbb{\red Q\pink{U}\purple{ES} \blue{T} \orange{IO}\green{N :}}$

A kite is flying with a thread of 150meters length from a field. If the thread of kite makes an angle 60° with the horizontal line, let us write by calculating the height of the kite from the ground.

$\huge\underline\mathbb{\red S\pink{O}\purple{LU} \blue{T} \orange{IO}\green{N :}}$

★ Given that,

• Length of kite (AB) = 150 meters.
• String makes an angle with the ground (∠B) = 60°.

★ To find,

• Height of the kite from ground (AC) = ?

★ Now,

↪ ABC is a right - angled triangle.

↪ By using suitable trigonometric ratio we can find out the height of the kite from ground.

★ So,

We show use " sine " ratio to get height.

★ We know that,

• sin θ = Opposite/Hypotenuse

↪ Opposite (AC) = x

↪ Hypotenuse (AB) = 150 meters.

↪ θ = 60° .

• Substitute the values.

$\sf\:⟹ sin \: 60° = \frac{x}{150}$

• sin 60° = √3/2

$\sf\:⟹ \frac{\sqrt{3}}{2} = \frac{x}{150}$

$\sf\:⟹ 150\sqrt{3} = 2x$

$\sf\:⟹ \frac{150\sqrt{3}}{2} = x$

$\sf\:⟹x = 75\sqrt{3}$

• √3 = 1.73

$\sf\:⟹ x = 75(1.73)$

$\sf\:⟹ x = 129.75$

$\underline{\boxed{\bf{\red{ ∴ Hence,height \: of \: kite \: from \: ground \: is 75\sqrt{3} \: meters \: or \: 129.75 \: meters.}}}}\:\orange{\bigstar}</p><p>$