1. Standing in an open field, Habul sees a flying bird at an angle of elevation of 30° towards the north, and after 2 minutes, he sees it at an angle of elevation of 60° towards the south. If the bird is flying along a straight horizontal path at a height of \(50\sqrt{3}\) meters, then calculate the speed of the bird.

2. Standing in the middle of the field, Rohit first saw a flying bird at an elevation angle of 30° towards the north, and then 2 minutes later, saw it at an angle of 60° towards the south. If the bird is flying along a straight path at a constant height of 50√3 meters, what is the bird’s speed in kilometers per hour?

3. A person first observes a bird flying at an angle of elevation of 60° towards the north, and after 5 minutes, sees it at an angle of elevation of 30° towards the south. If the bird is flying along the same straight line at a height of \(120\sqrt{3}\) meters, determine its speed in kilometers per hour.

4. Standing in the middle of a field, Mohit saw a flying bird—first to the north at an elevation angle of 30°, and then 2 minutes later to the south at an elevation angle of 60°. If the bird is flying along the same straight path at a height of 50√3 meters, calculate its speed in kilometers per hour.

5. Standing in the middle of a field, Mohit first sees a flying bird at an angle of elevation of 30° to the north. Two minutes later, he sees the same bird at an angle of elevation of 60° to the south. If the bird is flying along a straight line at a height of \(50\sqrt{3}\) meters, determine its speed in kilometers per hour.

6. Standing in the middle of a field, Mohit first saw a flying bird at an angle of elevation of 30° towards the north, and 2 minutes later, he saw it at an angle of elevation of 60° towards the south. If the bird was flying at a constant height of 50\(\sqrt{3}\) meters along a straight path, determine its speed in kilometers per hour.

7. Mohit observed a flying bird first at an elevation angle of 30° to the north, and then at an elevation angle of 60° to the south. If the bird was flying along a straight path at a height of \(50\sqrt{3}\) meters, calculate its speed in kilometers per hour.

8. Standing in the middle of a field, Mohit saw a flying bird—first to the north at an angle of elevation of 30°, and 2 minutes later to the south at an angle of elevation of 60°. If the bird is flying along the same straight line at a height of 50√3 meters, calculate its speed.

9. A bird was flying from north to south along a straight path parallel to the ground, at a height of 200 meters. Standing in the middle of a field, Sushovan first saw the bird at an angle of elevation of 30° towards the north. After 3 minutes, he saw it again at an angle of elevation of 45° towards the south. Find the bird’s speed in kilometers per hour, rounded to the nearest whole number. [Given: √3 ≈ 1.732]

10. A person observes an aircraft from a certain location at an angle of elevation of 60°. After 15 seconds, from the same location, he sees the aircraft again at an angle of elevation of 30°. If the aircraft is flying along the same straight line at a height of \(1500\sqrt{3}\) meters, then what is its speed?

11. A bird was flying from north to south along a path parallel to the ground at a height of 200 meters. Standing at the center of a field, Sushobhan first saw the bird at an angle of elevation of 30° to the north. Three minutes later, he again saw it at an angle of elevation of 45° to the south. Calculate and write the bird’s speed in kilometers per hour, rounded to the nearest whole number. [Take \(\sqrt{3} \approx 1.732\)]

12. A bird was flying from north to south along a path parallel to the ground at a height of 200 meters. Standing in the middle of a field, Payel first saw the bird at an angle of 30° to the north. Three minutes later, she saw it again at an angle of 45° to the south. Determine the speed of the bird.

13. If the angle of elevation of the top of a chimney from a point on level ground at its base is 60°, and from another point on the same straight line 24 meters further away from the base, the angle of elevation is 30°, then calculate and write the height of the chimney. [Take the approximate value of \(\sqrt{3} = 1.732\) and find the result correct to three decimal places.]

14. A person is positioned along a horizontal straight line on the same plane as a chimney. From a certain point, the angle of elevation to the top of the chimney is 30°. After moving 50 meters closer along the same straight path, the angle of elevation becomes 60°. Calculate and write the height of the chimney.

15. From a point on the roof of a five-story building, the angle of elevation to the top of a monument is 60°, and the angle of depression to its base is 30°. If the height of the building is 16 meters, then calculate and write the height of the monument and the distance of the building from the monument.

16. From a point on the roof of a five-story building, the angle of elevation to the top of a monument and the angle of depression to its base are 60° and 30° respectively. If the height of the building is 16 meters, what is the height of the monument?

17. From a point on the roof of a five-storey building, the angle of elevation to the top of a monument is 60°, and the angle of depression to its base is 30°. If the height of the building is 16 meters, find the height of the monument and the distance from the building to the monument.

18. From a point A on the ground, the angle of elevation to the top of a vertical pillar is 30°. After moving 20 meters toward the base of the pillar and reaching point B, the angle of elevation increases to 60°. Find the height of the pillar and the distance from point A to the pillar.

19. The heights of two pillars are 120 meters and 40 meters respectively. If the angle of elevation from the base of the second pillar to the top of the first pillar is 60°, then what is the angle of elevation from the base of the first pillar to the top of the second pillar?

20. From a point on the roof of a five-story building, the elevation angle to the top of a monument is 60°, and the depression angle to its base is 30°. If the building's height is 16 meters, determine the height of the monument and its distance from the building.

21. The heights of two pillars are 180 meters and 60 meters, respectively. If the angle of elevation to the top of the first pillar from the base of the second pillar is 60°, then determine the angle of elevation to the top of the second pillar from the base of the first pillar.

22. The heights of two towers are 180 meters and 60 meters, respectively. If the angle of elevation from the base of the second tower to the top of the first tower is 60°, then what is the angle of elevation from the base of the first tower to the top of the second tower?

23. From a point on the roof of a five-storied building, the angle of elevation to the top of a monument and the angle of depression to its base are 60° and 30° respectively. If the height of the building is 16 meters, find the height of the monument and the horizontal distance between the building and the monument.

24. Here's the full translation of your math problem into English: > The height of one building forms a right angle with the window of another building situated directly across the street. From that window, the angle of elevation to the top of the first building is 30°. > If the width of the street is \(4\sqrt{3}\) meters, find: > (1) the height of the first building, and > (2) how high the window of the second building is above the street level.

25. As the sun's angle of elevation increases from 30° to 60°, the length of the monument's shadow decreases by \(50\sqrt{3}\) meters. What is the height of the monument?

26. If the angles of depression from a lighthouse to two ships located along the same straight line are 60° and 30°, and the nearer ship is 150 meters away from the lighthouse, then what is the distance of the farther ship from the lighthouse?

27. From a ghat on one side of a 600-meter wide river, two boats set off toward the opposite bank in two different directions. If the first boat moves at an angle of 30° with the riverbank, and the second boat moves at a 90° angle to the path of the first boat, then what will be the distance between the two boats after they reach the opposite bank?

28. The heights of two pillars are 180 meters and 60 meters respectively. If the angle of elevation to the top of the second pillar from the base of the first pillar is 30°, then find the angle of elevation to the top of the first pillar from the base of the second pillar.

29. The deck of a ship is 10 meters above sea level. Standing on the deck, Apu observes the top of a lighthouse at an angle of elevation of 60°, and its base at an angle of depression of 30°. Find the distance from the ship to the lighthouse and the height of the lighthouse.

30. The heights of two pillars are \(180\) meters and \(60\) meters, respectively. The angle of elevation from the base of the second pillar to the top of the first pillar is \(60°\). Determine the angle of elevation from the base of the first pillar to the top of the second pillar.

(a) \(90°\) (b) \(60°\) (c) \(45°\) (d) \(30°\)