SOLUTION: Find the area of a 30 degree-60 degree-90 degree triangle with hypotenuse length of 48 inches.

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Question 388565: Find the area of a 30 degree-60 degree-90 degree triangle with hypotenuse length of 48 inches.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of all 30-60-90 right triangles are proportional. The hypotenuse is always twice the size of the side opposite the 30 degree angle. To put it the other way around, the side opposite the 30 degree angle is 1/2 the hypotenuse. Since this hypotenuse is 48, the side opposite 30 in this triangle will be half of that, or 24.

And the side opposite the 60 degree angle is always sqrt%283%29 times the side side opposite 30. We have found that the side opposite 30 in this triangle is 24. So the side opposite 60 will be sqrt%283%29%2A24 or 24sqrt%283%29.

The area of all triangles is %281%2F2%29bh. And for any right triangle you can use the two legs for a base and height. So the area of this triangle is:
%281%2F2%29%2824%29%2824sqrt%283%29%29 square inches
which simplifies to:
288sqrt%283%29 square inches