Question 489832: WHAT IS THE PERIMETER OF AN EQUILATERAL TRIANGLEWHOSE HEIGHT IS 2.33
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! The easiest way would be to use the law of sines.
We know that the angle opposite the 2.33 is 60 degrees, since this is an equilateral trianlge.
So, you can use the base of the triangle as the 30 degrees side, this will be 1/2 the side of the triangle.
2.33/ sin 60 = x/ sin 30
2.33(0.5) = 1.165 / 0.886 = 1.31. This will be 1/2 of one side, so one side will be 2.62.
The perimeter is 3(2.62) = 7.86.
You can also consider this an 90 degree triangle, again using the 30 degree angle we know the adjacent side to be 2.33 and we are looking for the hypotenuse.
So, tan 30 = opp / 2.33 = 1.345 *2 = 2.69, again one side of the triangle.
Cleomenius.
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