LUANDATO wrote:
What is the length of line segment AB in the figure above?
A. (√2)/2
B. (√3)/2
C. √2
D. 3/2
E. √3
If we drop a perpendicular from vertex A to side BC, that is, if we draw the height, we will divide the triangle into two special right triangles: a 45-45-90 triangle on the left and a 30-60-90 triangle on the right. Let's call this height AD, that is, D is a point on BC such that AD is perpendicular to BC.
We know that the side ratio of a 45-45-90 triangle is x : x : x√2. Since AC = 1, we see that if we let AD = x, then x√2 = 1. So x = 1/√2 = √2/2 = AD.
We also know that the side ratio of a 30-60-90 triangle is x : x√3 : 2x. Since AD = √2/2, we see that AB must be twice as much. So AB = 2(√2/2) = √2.
Answer:
C
