1. 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.

2. 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.

3. 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.

4. From a point on the roof of a five-storey building, the angle of elevation to the top of a monument and the angle of depression to its base are complementary angles. If the height of the monument is four times the height of the building, find the measures of the elevation and depression angles.

5. 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?

6. From the roof of an 18-meter-high five-story building, the angle of elevation to the top of a monument is 45°, and the angle of depression to its base is 60°. Find the height of the monument.

7. From a point on the roof of Shyamal’s five-storey building, the angle of elevation to the top of a monument is \(60^\circ\) and the angle of depression to the base of the monument is \(30^\circ\). > If the height of the building is 18 meters, then what is the height of the monument?

8. From the roof of a five-story building that is 18 meters high, the angle of elevation to the top of a monument is 45°, and the angle of depression to its base is 60°. Find the height of the monument.

9. From the roof and the base of a 16-meter high building, the angles of elevation to the top of a temple are 45° and 60°, respectively. Find the height of the temple and its horizontal distance from the building. (The base of the building and the temple lie on the same horizontal plane.)

10. If the angle of elevation to the top of a monument from the roof of a five-story building (18 meters high) is 45°, and the angle of depression to the base of the monument is 60°, then determine the height of the monument. (√3 = 1.732)

11. 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.

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

13. From the roof of a five-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°. What is the height of the monument?

14. 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.

15. 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.

16. 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.

17. A 5-meter-high house is located on one side of a park. From both the roof and the base of the house, the base and the top of a palm tree on the opposite side of the park are seen at angles of depression and elevation of 30° and 60°, respectively. What is the height of the palm tree? What is the distance between the house and the palm tree?

18. From the top of a building 60 meters high, the angles of depression to the top and bottom of a lamp post are 30° and 60°, respectively. Find: (i) The horizontal distance between the building and the lamp post (ii) The height of the lamp post

19. Two points on the ground lie along the same straight line with the base of a vertical pillar. From these two points, the angles of elevation to the top of the pillar are complementary. If the distances from the two points to the base of the pillar are 9 meters and 16 meters respectively, and both points are on the same side of the pillar, find the height of the pillar.

20. From the roof of a 15-meter-high house located at one end of a park, the base and top of a brick kiln chimney at the other end of the park are seen at angles of depression and elevation of 30° and 60°, respectively. Determine the height of the brick kiln chimney and the distance between the kiln and the house.

21. 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.]

22. From the roof of a 15-meter-high house situated at one end of a park, the foot and the top of a brick kiln chimney located at the other end of the park are seen at angles of depression and elevation of 30° and 60°, respectively. Find the height of the chimney and the distance between the brick kiln and the house.

23. From a point on the ground, the angle of elevation to the top of a mobile tower is 60°, and the distance from that point to the base of the tower is 10 meters. Find the height of the tower.

(a) 10 meters (b) 10\(\sqrt3\) meters (c) \(\frac{10}{\sqrt3}\) meters (d) 100 meters

24. A three-storey building has a flagpole of 3.6 meters mounted on its roof. From a point on the street, the angles of elevation to the top and bottom of the flagpole are 50° and 45°, respectively. Find the height of the building. [Assume: \(\tan 50^\circ = 1.2\)]

25. A flag of 3.3 meters in length is mounted on the roof of a three-story building. From a certain point on the street, the angles of elevation to the top and bottom of the flagpole are 50° and 45°, respectively. Determine the height of the building. [tan 50° = 1.192]

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

27. From the roof of an 11-meter-high building, the angles of depression to the top and base of a lamppost are 30° and 60°, respectively. Find the height of the lamppost.

28. From the rooftop of a three-story building that is \(9\sqrt{3}\) meters high, the angle of elevation to the top of a factory chimney located 30 meters away is 30°. Calculate and write the height of the chimney.

29. A 3.3-meter-long flag is placed on the rooftop of a three-story building. From a point on the street, the angles of elevation to the top and bottom of the flagstaff are 50° and 45°, respectively. Calculate the height of the building. [Assume \(\tan50° = 1.192\)]

30. From two points located on the same side and along the same horizontal line passing through the base of a vertical pillar, the angles of elevation to the top of the pillar are respectively \(\theta\) and \(\phi\). If the height of the pillar is \(h\), find the distance between the two points.