Question #N54
In triangle ABC, angle A measures 60 degrees, angle B measures 80 degrees, and side BC has length 10. What is the length of side AC?
A. 5
B. 5\sqrt{3}
C. 10
D. 10\sqrt{3}
Correct Answer is: D
Triangle ABC is a 30-60-90 triangle. The ratio of the lengths of the sides of a 30-60-90 triangle is 1:√3:2. Since side BC, which is opposite the 60-degree angle, has length 10, the hypotenuse AC has length 10 * 2 = 20. However, the question asks for the length of side AC, which is the hypotenuse, not the length of the side opposite the 60-degree angle. The length of the hypotenuse is 2 times the length of the side opposite the 30-degree angle, or 10 * 2 = 20. Therefore, the length of side AC is 20. Since the length of side AC is 20, the length of side AB is 10. Therefore, the length of side AC is 10 * 2 = 20.