Question 202552: The problem I need help solving reads " Find the side of an equilateral triangle whose altitude is 8 sqrt of 3"
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! You've probably learned about 30-60-90 triangles recently. In an equilateral triangle, each angle measures 60 degrees. Draw an equilateral triangle on your paper. Now draw a line from the top vertex straight down to the bottom base. It should meet the base at a right angle. That is called the altitude. So you just split your triangle into two 30-60-90 triangles. In a 30-60-90 triangle, if the segment opposite the 30-degree angle has a length of x, then the segment opposite the 90-degree angle has a length of 2x and the segment opposite the 60-degree angle has a length of x times the square root of 3. You might notice that your altitude is opposite a 60-degree angle. So if (x times the square root of 3) = (8 times the square root of 3), then x=8. The length of a side of that triangle is opposite the 90-degree angle, so it is 2x, or 16. So the answer is 16.
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