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