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1. The triangle has three sides equal, so that each inner angle is 60°
2. The altitude, forms a right angle to the opposite side, so that there are two new right triangles whose interior angles are 90°, 60° and 30°
For each angle of 60°, in the new triangles, we can write that:
sine 60°= opposite side/hypotenuse
opposite side = Altitude of the equilateral triangle.
hypotenuse = side of the equilateral triangle (what we are looking)
Then we can write:
sine 60°= 9/hypotenuse
hypotenuse = side of the equilateral triangle = 9/0.866 = 10.39 m
The formula for that solution is
A = (2/sqrt of 3) x h
I couldn't figure out the formula button on this website.
A = side length. Since you have an equilateral triangle, all of the sides will be equal.
h = altitude of your triangle, which you stated is 9 meters
sqrt = square root.
So with your numbers, it looks like this
A = (2/sqrt of 3) x 9
A = 10.3923 meters.
Once you know "A" you can figure out a lot of other stuff about the triangle. Multiply it by 3 to get the perimeter.
The semiperimeter of the triangle would be (3A)/2
The area would be 1/4 * sqrt 3 * A^2
Of course those formulas only work as long as your triangles continue to be equilateral triangles.
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