what's the area in square units of triangle ABC?

Question

In triangle ABC, the measure of angle A is 60 degrees and the measure of angle B is 30 degrees. If line AB is 8 units long, what's the area in square units of triangle ABC?

Answer 1

Remember what I now tell you, because 30-60-90 triangles abound in math courses and in the SAT.

 

You've been told that the hypotenuse length is 8.  In EVERY 30-60-90 triangle, the side opposite the 30degree angle has length ½ of the hypotenuse--this is the 'short leg.'  Then the long leg = short leg times √3.

 

Therefore we can say base (short leg) is4, height is 4√3, and using the formula ½•base•height for area of the triangle, we obtain the area 8√3 square units.