To find the length of the string of the kite, we need to apply basic trigonometry, utilizing the concept of the angle of elevation. Given that the kite is at an altitude of 75 meters above the ground and the angle of elevation of the string with the ground is 30 degrees, we can use the sine function, which relates the opposite side (altitude) of the angle in a right-angled triangle to the hypotenuse (length of the string). Here's how we can solve it step-by-step:
- Identify the components of the problem in terms of a right triangle. The sides involved are:
- Opposite side (altitude of the kite) = 75 meters
- Angle of elevation = 30 degrees
- Hypotenuse = Length of the string (unknown)
- Use the sine ratio in the right triangle: \(\sin(\theta) = \frac{\text{Opposite side}}{\text{Hypotenuse}}\)
- Substitute the given values into the sine formula: \(\sin(30^\circ) = \frac{75}{\text{Hypotenuse}}\)
- We know that \(\sin(30^\circ) = 0.5\). Substitute this value: \(0.5 = \frac{75}{\text{Hypotenuse}}\)
- Cross multiply to solve for the hypotenuse: \(\text{Hypotenuse} = \frac{75}{0.5} = 150 \, \text{meters}\)
- Thus, the length of the string is 150 meters.
Therefore, the correct answer is 150 m.
Similar Questions
- A 5-foot person casts a 4-foot shadow. At the same time, a tree casts a 20-foot shadow. How tall is the tree?
- The angles of elevation of the top of a cliff from two points on the ground, $200\text{ m}$ apart, and on opposite sides of the cliff, are $30^{\circ}$ and $45^{\circ}$. What is the height of the cliff?
A man observes the top of a pole with an angle of elevation of 45°. He walks 15 m towards the pole, and the angle of elevation becomes 60°. What is the height of the pole?
Two ships positioned on opposite sides of a lighthouse observe the angles of elevation to the top of the lighthouse, which are 30° and 45° respectively. Given that the height of the lighthouse is 100 meters, determine the distance between the two ships.
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?
