Question

Solved previously.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

Answer 1

6√3 square units

Explanation:

The ratios of side lengths in a 30°-60°-90° triangle are 1 : √3 : 2. Using this fact, we can find the lengths of the orthogonal sides of the triangle to be ...

3(2/√3) = 2√3 . . . . side AB in the attached figure

and

2·3 = 6 . . . . . . . . . . side AC in the attached figure

Then the area of the triangle is ...

A = 1/2bh

A = 1/2(6)(2√3) = 6√3 . . . . square units