Home » Test Prep » ACT Section 2: Math » Which means that the length of the hypotenuse, AC, is equal to twice the length ofthe 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 v3 times the length of the other leg, BC. Therefore, the length of AB is 5√3.
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. 
Correct Answer: C
Explanation/Reference: 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 ofthe 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 v3 times the length of the other leg, BC. Therefore, the length of AB is 5√3.
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