Which makes triangle EDC a 30-60-90 right triangle. The leg opposite the 60-degree angle is equal to v3 times the length of the leg opposite the 30-degree angle.

In the diagram above, FDCB is a rectangle. Line ED is six units long, line AB is ten units long, and the measure of angle ECD is 60º. What is the length of line AE?

A. 8
B.

C. 20
D.

E.

Correct Answer: E
Explanation/Reference: Explanation:
FDCB is a rectangle, which means that

is a right angle.
is 60º, which makes triangle EDC a 30-60-90 right triangle. The leg opposite the 60-degree angle is equal to v3 times the length of the leg opposite the 30-degree angle.
Therefore, the length of side DC is equal to

, or 2√3. The hypotenuse of a 30-60-90 right triangle is equal to twice the length of the leg opposite the 30-degree angle, so the length of EC is 2 x 2√3 = 4√3.
is also a right angle, and triangle ABC is also a 30-60-60 right triangle. Since

is 60º,

is equal to 90 – 60 = 30º. Therefore, the length of AC, the hypotenuse of triangle ABC, is twice the length of AB: 2 x 10 = 20. The length of AC is 20 and the length of EC is 4√3. Therefore, the length of AE is 20 – 4√3.

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