SAT Subject Test Mathematics Level 2

Example 3

Figure  3

To get the answer to this question, you need to know about equilateral, 45-45-90, and 30-60-90
triangles. If you drop an altitude from a new point, N, through M to L, you will divide the equilateral
triangle into two 30-60-90 triangles and divide the right isosceles (or 45-45-90) triangle into two
smaller right isosceles triangles:

Using the side ratios for 30-60-90s and 45-45-90s, you know that and that = 1.

Therefore,

In  Figure  3,  ∆JKL    is  equilateral,    and ∆JKM    is  isosceles.  If      =   2,  what    is  the distance    from    L

to  M?

1.

(A) 0.572

(B) 0.636

(C) 0.667

(D) 0.732

(E) 0.767