## anonymous one year ago a segment of a circle has a 120 degree arc and a chord of 8 to the square root of 3 inches. find the area of the segment.

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1. amistre64

what does "8 to the square root of 3" mean?

2. amistre64

$8^{(\sqrt 3)}$ ??

3. anonymous

$8\sqrt{3}$ this is what it looks like in the problem

4. amistre64

thats: 8 square roots of 3 then, no "to" required

5. amistre64

terminology ... what is a segment?

6. anonymous

the part of a figure cut off by a line

7. amistre64

so instead of a slice of pizza, its just the crust right?

8. anonymous

yes, basically

9. amistre64

ok, i get those mixed up alot. so we want the area of the slice, minus the area of the triangle .. any ideas?

10. amistre64

|dw:1436478599531:dw|

11. amistre64

do we know trig? or special triangles?

12. anonymous

no, we do not

13. amistre64

well, without trig or some knowledge of special triangles, we really cant approach this.

14. amistre64

the special triangle we would need to know about is a 30-60-90 degree

15. anonymous

so then how would we apply that to an equation?

16. amistre64

if you have formulas at your disposal, then you might be able to use them .. but i do not know what you have available to you. hence my thought to use a 30-60-90 special triangle

17. amistre64

|dw:1436478952947:dw|

18. anonymous

area of segment=area of sector-area of triangle

19. amistre64

ideally we learn, that a 30-60-90 can be constructed from an equilateral triangle, where all the sides are the same length |dw:1436479033334:dw| using the pythagorean thrm, we find that the missing side is sqrt(3) giving us the special ratio of: |dw:1436479105655:dw|

20. amistre64

in your case, we can then use it to scale to the desired length |dw:1436479181984:dw|

21. amistre64

but if you have no knowledge of this, then i dont see much of a way to approach a solution

22. amistre64

|dw:1436479458168:dw| we have 120/360 of the area of the circle (pi 8^2) and we have 2 triangles (a rectangle is 2 triangles) of base 4, and height 8sqrt(3)

23. amistre64

height of 4sqrt(3) THAT IS

24. amistre64

as i mentioned, without some trig or knowledge of the special 30-60-90 triangle, i see no way to approach this problem ...

25. anonymous

okay well thank you for trying