I need help with a simple function problem.?

Question

If the problem is "The height of an equilateral triangle as a function of its side length" And the directions are to write a formula that expresses the first variable as a function of the second.
I understand slightly what to do, but I need some help.

Answer 1

Ok, let's say x is the variable : it's the side length.
Then f(x) will be the height of your triangle.
You'll have:

f(x) = SquareRoot(x²-(x²)/4)

The demonstration is the following:
Let's say f(x)=y
You know that (x/2)² + y² = x² (Pythagorus)
then x²/4 + y² = x²
y = SquareRoot ( x² - x²/4 )

Answer 2

An equilateral triangle has 60 degree angles.
Let the side length be x, then the height is (sqrt(3)/2)x
That is,
H(x) = (sqrt(3)/2)x
In words, To find the height of an equilateral triangle, you divide the side length by 2 and multiply by the square root of 3.

Answer 3

Well if you have an equalateral triangle then each angle is 60 degrees. So if the lengthis 20 on each side then the height will be 2/3 thirds of the length of the side. If it was twenty then it is 20 multiplied by 2/3.

Answer 4

the height would be 'H', side would be 'S' and half the length would be 'L'.

The formula is (H)^2 + (L)^2 = (S)^2 or

H = sqrt[(S)^2 - (L)^2]

the dividing line (or height) creates two right triangles, so the side becomes the hypotenuse, the bottom (L) is one side of the right triangle (which is half the originial length) and the height is the other side of the right triangle. So the formula for this is (one side squared) + (the other side squared) = (the side opposite the 90 degree angle squared)

Answer 5

Here's how I solve it. Let s = side length, y = height

Bisect your triangle and you get two right triangles. With this formula:

s^2 = (s/2)^2 + y^2

So y^2 = s^2 - (s/2)^2
which is also
y^2 = s^2 - s^2/4
y = s * sqrt(3/4)

Answer 6

i just read the first three answers, all of them are right.

height = (half of sq.rt 3) X the length of the sides of the eq. triangle