1. Standing in the middle of the field, Habu sees a flying bird first at an elevation angle of 30° to the north, and after 2 minutes, at an elevation angle of 60° to the south. If the bird is flying along a straight path at a constant height of \(50\sqrt{3}\) meters, then what is its speed?

2. 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.

3. 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?

4. 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.

5. 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.

6. 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.

7. 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.

8. 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]

9. 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.

10. 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 \(\sqrt{3} \approx 1.732\)]

11. 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?

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. 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.

14. 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.]

15. Suppose a passenger on an airplane, at a certain moment, sees Howrah Station on one side and Shaheed Minar on the exact opposite side, with angles of depression of 60° and 30° respectively. At that time, if the airplane is flying at a height of \(545\sqrt{3}\) meters, then determine the distance between Howrah Station and Shaheed Minar.

16. 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.

17. If the elevation angle of a kite is 60° and the length of the string is 20√3 meters, calculate the height of the kite above the ground.

18. If the elevation angle of a kite is 60°and the length of the string is 20√3 meters, calculate the height of the kite from the ground.

19. 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.

20. If from the roof of a 5-storey building that is 18 meters high, the angle of elevation to the top of a monument is 45° and the angle of depression to the base of the monument is 60°, then calculate and write the height of the monument. [Take \(\sqrt{3} \approx 1.732\)]

21. If the angles of depression from the top of a lighthouse to the bases of the masts of two ships situated along the same straight line are 60° and 30° respectively, and the nearer ship is 150 meters away from the lighthouse, then calculate the distance of the farther ship from the lighthouse and the height of the lighthouse.

22. 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.

23. A passenger on an airplane once saw Howrah Station on one side and Shaheed Minar on the opposite side at angles of depression of 60° and 30°, respectively. At that moment, if the airplane was flying at a height of \(545\sqrt{3}\) meters, what is the distance between Howrah Station and Shaheed Minar?

24. 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.

25. 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.

26. A person in an airship sees Howrah Station and, directly opposite, the Shaheed Minar at angles of depression of 60° and 30°, respectively. If the airship is at a height of \( 545\sqrt{3} \) meters, find the distance between Howrah Station and Shaheed Minar.

27. If from the roof of a 5-storey building that is 18 meters high, the angle of elevation to the top of a monument is 45°, and the angle of depression to the base of the monument is 60°, then calculate the height of the monument. (Take √3 ≈ 1.732) Let me know if you'd like a step-by-step solution as well.

28. If the angle of elevation of the top of a coconut tree from a point on the horizontal ground 20 meters away from its base is 60°, then find the height of the tree.

29. If the angle of elevation of a kite is 60° and the length of the string is \(20\sqrt{3}\) meters, find the height of the kite above the ground.

30. Here is the English translation: > Two pillars of equal height are located directly opposite each other at points A and B on either side of a 120-meter wide road. From point C, on the line joining their bases, the angles of elevation to the tops of the pillars at A and B are 60° and 30°, respectively. Find the length of AC.