What is the length of line AB?

In the diagram above, lines EF and GH are parallel, and line AB is perpendicular to lines EF and GH.

What is the length of line AB?
A . 5
B .

C .


D .

E .

View Answer

Answer: C

Explanation:

Line AB is perpendicular to line BC, which makes triangle ABC a right triangle.

and

are

alternating angles, i.e. angles made by a pair of parallel lines cut by a

transversal.

, therefore,

.

form a line. There

are 180º in a line, so the measure of of

. Triangle ABC is a 30-60-90 right triangle, which means that the length of the hypotenuse, AC, is equal to twice the length of the leg opposite the 30-degree angle, BC. Therefore, the length of BC is 10/2, or 5. The length of the leg opposite the 60-degree angle, AB, is √3 times the length of the other leg, BC. Therefore, the length of AB is 5√3.