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.
+129849 We can split the base into two parts....m and n
tan 30° = 3 /m
sqrt (3) / 3 = 3/m
m = 3 / ( sqrt (3) / 3)
m = 9 / sqrt (3) = 3 sqrt (3)
tan 60° = 3 / n
sqrt (3) = 3 / n
n = 3 /sqrt (3) = sqrt (3)
So....area =
(1/2) base length * height =
(1/2) (m + n) * height =
(1/2) (3sqrt (3) + sqrt (3) )* 3 =
(1/2) ( 4 sqrt (3) ) * 3 =
2sqrt (3) * 3 =
6sqrt (3) (square units)
