SOLUTION: I posted before. Could I get steps on how to solve this. If possible algebraically, I have to know how to solve it without a calculator. Solve for x (x=AB) in the figure shown

Algebra ->  Finance -> SOLUTION: I posted before. Could I get steps on how to solve this. If possible algebraically, I have to know how to solve it without a calculator. Solve for x (x=AB) in the figure shown       Log On


   

Question 960990: I posted before. Could I get steps on how to solve this. If possible algebraically, I have to know how to solve it without a calculator.
Solve for x (x=AB) in the figure shown
CD=200
http://i.imgur.com/PqcA5E3.png

Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find BD:
Angle ABC+=+90 degrees
tan%2830%29+=+BD%2F200
1%2Fsqrt%283%29+=+%28BD%29%2F200
BD=200%2Fsqrt%283%29+...exact
BD=115.47 .....approximately
Then,
sin%2860%29+=+BD%2Fx
x+=+BD%2Fsin%2860%29
x+=+115.47%2F%28sqrt%283%29%2F2%29
x+=+115.47%2F0.8660
x+=+133.3332711666522
x+=+133.33....approximately

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I posted before. Could I get steps on how to solve this. If possible algebraically, I have to know how to solve it without a calculator.
Solve for x (x=AB) in the figure shown
CD=200
http://i.imgur.com/PqcA5E3.png 
From ∆BDC, tan ∠DBC = O%2FA

tan+60%5Eo+=+DC%2FBD

tan+60%5Eo+=+200%2FBD

BD+%2A+tan+60%5Eo+=+200 ------- Cross-multiplying

BD+=+200%2Ftan+60%5Eo

BD+=+200%22%F7%22%28sin+60%5Eo%2Fcos+60%5Eo%29 ------ tan+60%5Eo+=+%28sin+60%5Eo%29%2F%28cos+60%5Eo%29

BD+=+200%22%F7%22%28sqrt%283%29%2F2%29%2F%281%2F2%29 ------ sin+60%5Eo+=+sqrt%283%29%2F2 and cos+60%5Eo+=+1%2F2

BD+=+200%22%F7%22(sqrt%283%29%2F2%22%F7%221%2F2)

BD+=+200%22%F7%22(sqrt%283%29%2F2%22%2A%222%2F1)

BD+=+200%2Fsqrt%283%29, or 200sqrt%283%29%2F3



From ∆ABD, sin ∠BAD = O%2FH

sin+60%5Eo+=+BD%2FAB

sin+60%5Eo+=+BD%2Fx 

sin+60%5Eo+=+%28200sqrt%283%29%2F3%29%2Fx

x+%2A+sin+60%5Eo+=+%28200sqrt%283%29%29%2F3 --------- Cross-multiplying

x+=+200sqrt%283%29%2F3%22%F7%22sin+60%5Eo

x+=+200sqrt%283%29%2F3%22%F7%22sqrt%283%29%2F2

x+=+200sqrt%283%29%2F3%22%2A%222%2Fsqrt%283%29

x+=+200cross%28sqrt%283%29%29%2F3%22%2A%222%2Fcross%28sqrt%283%29%29

AB, or highlight_green%28x+=+400%2F3%29