The altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.
Using the "Law of Sines" we have:
The hypotenuse of the large triangle =4sqrt(3)
The shorter side to the right =2sqrt(3)
The Base to the left =6
Area of the large triangle =1/2 x 6 x 2sqrt(3) =6sqrt(3) units^2.
The triangle on the "left" has a base = 3sqrt (3)
The triangle on the "right" has a base = 3 / sqrt (3) = 3sqrt (3) / 3 = sqrt (3)
So.....the area =
(3) [ 3 sqrt (3) + sqrt (3) ] / 2 =
3 [ 4sqrt (3) ] / 2 =
3 [ 2 sqrt (3) ] =
6sqrt (3) units^2
+4 
