What is the length of side DC?

In the diagram above, ABC and DEC are right triangles, the length of
side BC is 15 units, and the measure of is 60º. If

is congruent to

, what is the length of side DC?
A. √15 units
B. 15/2 units
C. 15/2 x √3 units
D. 9 units
E. 15√3 units

Correct Answer: B
Explanation/Reference: Explanation:
Since triangle DEC is a right triangle, triangle AED is also a right triangle, with a right angle at AED. There are 180º in a triangle, so the measure of is
180 – (60 + 90) = 30º. and are congruent, so is also 60º. Since there are 180º in a line,
must be 90º, making triangle BDC a right triangle. Triangle ABC is a right triangle with measuring 60º0, which means that must be 30º, and BDC must be a 30-60- 90 right triangle. The leg opposite the 30-degree angle in a 30-60-90 right triangle is half the length of the hypotenuse. Therefore, the length of DC is 15/2 units.

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