1. Find Line Segment AB

In right triangles ABC and EDC, we have line segment BCD, AC is perpendicular to EC, BD = 10, CE = 8 and the measure of angle ACB = 30 degrees. What is the length of line segment AB?

(a) 2(sqrt{3})

(b) 3

(c) 3(sqrt{3})

(d) 6

I selected choice (d) but the book's answer is choice (a).

2. Originally Posted by sharkman
In right triangles ABC and EDC, we have line segment BCD, AC is perpendicular to EC, BD = 10, CE = 8 and the measure of angle ACB = 30 degrees. What is the length of line segment AB?

(a) 2(sqrt{3})

(b) 3

(c) 3(sqrt{3})

(d) 6

I selected choice (d) but the book's answer is choice (a).
is there a diagram with the question?

3. yes..

Originally Posted by skeeter
is there a diagram with the question?
Yes, but I don't know how to draw it here.

4. Originally Posted by sharkman
Yes, but I don't know how to draw it here.
sketch it using windows "paint" and upload as an attachment.

5. Originally Posted by sharkman
In right triangles ABC and EDC, we have line segment BCD, AC is perpendicular to EC, BD = 10, CE = 8 and the measure of angle ACB = 30 degrees. What is the length of line segment AB?

(a) 2(sqrt{3})

(b) 3

(c) 3(sqrt{3})

(d) 6

I selected choice (d) but the book's answer is choice (a).
This is my first trial of using "paint"

If that is correct:
$\displaystyle \angle ECD = 60deg$
CD = 8 cos(60deg) = 4
&
AB = (10-4)tan(30deg) = $\displaystyle 2\sqrt{3}$

6. Thanks

Thank you all for the help.

7. ok..

Originally Posted by skeeter
sketch it using windows "paint" and upload as an attachment.
I did not know I can do that here.

Thanks

8. yes..

Originally Posted by aidan
This is my first trial of using "paint"

If that is correct:
$\displaystyle \angle ECD = 60deg$
CD = 8 cos(60deg) = 4
&
AB = (10-4)tan(30deg) = $\displaystyle 2\sqrt{3}$
That is correct!