## anonymous one year ago 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 60 degrees and angle BDC measures 30 degrees. The length of DC is 5 multiplied by square root of 3. Angle ADC measures 60° and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?

1. anonymous

can anyone help me out with this

2. anonymous

the answer choices are 10, 15, 20, and 25

3. campbell_st

is C the base of the flagpole..?

4. anonymous

5. campbell_st

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6. anonymous

i posed a picture of the triangle

7. campbell_st

so find the length AC using the tan ratio and an angle of 60 then find BC, again using the tan ratio and an angle of 30 the the distance AB is AC - BC hope it helps

8. anonymous

thank you! wait is the answer 10ft?

9. campbell_st

I don't know I haven't done the calculation

10. anonymous

can you walk me through it

11. campbell_st

ok... so do you know the exact value of tan(30) and tan(60)..?

12. anonymous

tan60 is 1.73205080757

13. anonymous

tan30 is 0.57735026919

14. campbell_st

here is the start$\tan(60) = \frac{AC}{5 \sqrt{3}}~~~then~~~AC = 5 \sqrt{3} \times \tan(60)$ and $\tan(30) = \frac{BC}{5\sqrt{3}}~~~~~then~~~~BC = 5\sqrt{3} \times \tan(30)$ hope it helps

15. campbell_st

last step AB = AC - BC

16. anonymous

i got 20ft?

17. campbell_st

I think you need to check the calculations

18. anonymous

ok let me check

19. anonymous

ohhhhh ok so now i see what i did wrong is the answer 15?

20. campbell_st

well AC is 15 now calculate BC

21. anonymous

so bc is 5 right?

22. campbell_st

yes

23. anonymous

that would mean the answer is 10 right?

24. campbell_st

correct

25. anonymous

THANK SO MUCH !!!!!!!