Kite Height Calculation Using Trigonometry
This problem involves finding the vertical height of a kite using the length of the string and the angle it makes with the ground. We can model this situation using a right-angled triangle.
- The kite string represents the hypotenuse of the triangle.
- The angle the string makes with the ground is given.
- The height of the kite is the side opposite to this angle.
We use the sine trigonometric function, which relates the angle, the opposite side (height), and the hypotenuse (string length).
The formula is:
$ \text{Height} = \text{String Length} \times \sin(\text{Angle}) $
Given:
- String Length ($L$) = 24.4 m
- Angle ($\theta$) = 30°
Calculation:
$ h = L \times \sin(\theta) $
$ h = 24.4 \text{ m} \times \sin(30^\circ) $
We know that $ \sin(30^\circ) = 0.5 $. Therefore:
$ h = 24.4 \text{ m} \times 0.5 $
$ h = 12.2 \text{ m} $
The height of the kite from the ground is 12.2 m.
Important Questions from Heights and Distances
If x is the distance of P from the bottom of the pillar, then consider the following statements :
1. x can take two values which are in the ratio 1 : 3
2. x can be equal to the height of the flagstaff
Which of the statements given above is/are correct?
What is a possible value of tan θ ?
A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30° and 45° respectively. Which one of the following gives the best approximation to the height of the tower?
Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15° with the horizontal. The distance between the poles is approximately equal to
The angle of elevation of the top of a tower from a point 20 m away from its base is 45 °. What is the height of the tower?
