Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole, as shown below: Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole. Angle ADC measures 45 degrees, and angle BDC measures 30 degrees. The length of DC is 5 multiplied by square root of 3. Angle ADC measures 45°, and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?. A. 3.66 feet B.13.66 feet C. 8.66 feet D. 5 feet

  A.  3.66 feet

Step-by-step explanation:

Using trigonometry, we know that ...

  BC = DC·tan(30°)

  AC = DC·tan(45°)

  AB = AC -BC = DC(tan(45°) -tan(30°))

  AB = 5√3·(1 -√3/3) = 5(√3 -1)

  AB ≈ 3.66 . . . feet

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: