1. lolly

2. amistre64

in order for the line to be 8, the angle has to be greater than zero

3. amistre64

oh ... its an equation in x ... thought x was the angle at first

4. amistre64

i would say that 5x+3 has to be less than 58

5. lolly

sooo...how do you find x? or what am i supposed to be finding?

6. amistre64

well, we want the angle to be greater than 0 and less than 58; so solve those 2 conditions to find your limits

7. amistre64

5x+3 > 0 and 5x+3 < 58

8. amistre64

58 corresponds to 11, which is what the left side is telling us; and the right side say in order to be 8, the angle needs to be bigger than zero, since and angle of zero gives us a zero length

9. lolly

soo which one would it be?

10. amistre64

youll have to do the math from the equation i gave you ...

11. amistre64

5x+3 > 0 and 5x+3 < 58 solve x for each case

12. lolly

whats the first step?

13. lolly

minus 3 from each side?

14. amistre64

yes, minus 3 then divide off the 5

15. nickersia

Ok here is what I think :) AB = BC BD = BD So those two triangles ABD and BCD have two same sides. ABD got third side 11, and opposite angle 58 BCD got third side 8, and oppsoite angle 5x+3 So we can use proportion 11:58=8:(5x+3) 55x+33=464 55x=431 x=7.84 Something around, I'm not sure does x has to be that number, any way you have options, which makes it easier... A is not for sure, because it is almost impossible when sides BD and BC are same as in ABD triangle, and the side is 8, to use 0.00000001 for x, which will be aroud 3 degrees... B got negative value, same story C smallest number will make angle bigger that 58 degrees, so not this one too D is the right answer, I think I hope I helped you, this was a really hard one... Enjoy and good luck! :)