# Thread: Finding the length of segment

1. ## Finding the length of segment

This one has been eating at me for a long time and I just can't figure it out:

In the figure below, ACDF is a parallelogram. Segment AE is perpendicular to line CD, and segment DB is perpendicular to line AC. The length of DB is 6 meters, segment FA is 9 meters and segment AC is 15 meters. How many meters long is segment AE?

How do I show/prove that it's 10 meters?

2. Originally Posted by harold
This one has been eating at me for a long time and I just can't figure it out:

In the figure below, ACDF is a parallelogram. Segment AE is perpendicular to line CD, and segment DB is perpendicular to line AC. The length of DB is 6 meters, segment FA is 9 meters and segment AC is 15 meters. How many meters long is segment AE?

How do I show/prove that it's 10 meters?
1. Calculate the sinus of the angle at C in the right triangle BCD:

$\sin(C)=\frac69$

2. Calculate the sinus of the angle at C in the right triangle ACE:

$\sin(C)=\frac69=\frac{\overline{AE}}{AC}$

3. Plug in all values you know: AC = 15, sin(C) to calculate

$|\overline{AE}| = \frac69 \cdot 15 = 10$

3. Thanks so much earboth--it was driving me crazy!!

4. Alternatively, you could recognize the similar triangles, so therefore

(9/15) = (6/x), thus x=10