1. 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?

2. The English translation is: "When the sun's angle of elevation increases from 45° to 60°, the length of the shadow of a pole decreases by 3 meters. Determine the height of the pole. (Take \(\sqrt{3} = 1.732\))"

3. When the sun's elevation angle increases from 45° to 60°, the length of the shadow of a pole decreases by 3 meters. Find the height of the pole. [Take √3 = 1.732 and calculate the approximate value up to three decimal places.]

4. When the sun's elevation angle increases from 45° to 60°, the length of a pole's shadow decreases by 3 meters. Find the height of the pole.

(a) 7.1 meter (b) 9 meter (c) 10 meter (d) 11 meter

5. If the sun's elevation angle increases from 45° to 60°, the length of a pole's shadow decreases by x meters. Determine the height of the pole, assuming √3 = 1.732, rounded to three decimal places.

6. When the sun's elevation angle increases from 45° to 60°, the length of a post's shadow decreases by 3 meters. Determine the height of the post.

7. When the sun's angle of elevation is 45°, the length of the shadow of a vertical pillar on a horizontal plane is a certain value. When the angle of elevation becomes 30°, the shadow length increases by 60 meters compared to the previous case. Find the height of the pillar.

8. When the elevation angle of the Sun increases from 45° to 60°, the length of a pole's shadow decreases by 3 meters. Determine the height of the pole (√3 = 1.732).

9. If the sun's altitude angle increases from 45° to 60°, the length of a pole's shadow decreases by 3 meters. Determine the height of the pole. Given, \( \sqrt{3} = 1.732 \).

10. When the sun's angle of elevation changes from 45° to 60°, the length of the shadow of a telegraph pole changes by 4 meters. Determine the length of the shadow when the angle of elevation is 30°.

11. If the sun's angle of elevation increases from 45° to 60°, the shadow of a pole shortens by 3 meters. Determine the height of the pole.

12. When the angle of elevation of the sun increases from 45° to 60°, the length of a pole’s shadow shortens by 3 meters. Determine the height of the pole. [Take \(\sqrt{3} = 1.732\) and find the approximate value correct to three decimal places.]

13. When the sun’s angle of elevation changes from 45° to 60°, the shadow of a telegraph pole changes by 4 meters. Find the length of the shadow of the same pole when the angle of elevation is 30°.

14. When the sun's elevation angle increases from 30° to 60°, the length of a post's shadow — decreases.

15. When the angle of elevation of the sun is 45°, the length of the shadow of a vertical pillar is a certain value. When the angle of elevation decreases to 30°, the length of the shadow becomes 60 meters longer than before. Determine the height of the pillar.

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. When the angle of elevation of the Sun increases from 30° to 60°, the length of the shadow of a post ______. (decreases/increases)

18. 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.

19. There is a flagpole on top of a monument. When the sun’s elevation angle is 30°, the shadow length of the flagpole is 3√3 meters. > What is the height of the flagpole? > If the height of the monument is 15 meters, then what will be the total shadow length of the monument including the flagpole?

20. A 30-meter high pole and a pillar are located on the same horizontal plane. The foot of the pillar is seen from the top of the pole at a depression angle of 30°, and the top of the pillar is seen from the base of the pole at an elevation angle of 60°. What is the height of the pillar and the distance between the pole and the pillar?

21. 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?

22. If the sun's elevation angle is _____, then the length of the pillar's shadow will be equal to the height of the pillar.

23. The heights of two pillars are 180 meters and 60 meters. If the angle of elevation from the base of the second pillar to the top of the first pillar is 60°, what is the angle of elevation from the base of the first pillar to the top of the second pillar?

24. 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.

25. When the angle of elevation of the sun is 30°, the length of the shadow of a pillar is 9 meters. Find and write the height of the pillar.

26. 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.]

27. 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

28. From the top and the base of a vertical mountain, the angles of depression and elevation to the top of a 30-meter high pillar are respectively 30° and 60°. What is the height of the mountain?

29. The translation is: **Two vertical pillars** of heights \(h_1\) and \(h_2\) units stand on the same horizontal plane. From the foot of the pillar of height \(h_1\), the angle of elevation to the top of the other pillar (of height \(h_2\)) is 60°, and from the foot of the pillar of height \(h_2\), the angle of elevation to the top of the pillar of height \(h_1\) is 45°. Prove that: \(h_1^2 = 3h_2^2\)

30. When the sun's angle of elevation changes from 30° to 60°, the length of a post's shadow becomes half.