triangles????

Question

What is the formula for finding the height of an equalateral triangle?

....................................... r0ck 0n ...................................................

Answer 1

height = base * sqrt(3) / 2

Let me show you why:

An equilateral triangle has all sides the same, and all angles = 60 degrees.

So, if you draw a line from the top of the triangle straight down to the bottom, you'll see that you've divided the triangle in half into two equal, right-angled triangles.

Now, I'm going to skip a little bit of explanation here and ask you to notice that the two triangles are 30-60-90 triangles, which means that the sides of the triangle bear a ratio of 1:2:sqrt(3) where 1 is the base, 2 is the hypotenuse, and sqrt(3) is the line that the two new triangles share.

So, take that ratio between the bottom side of the triangle (this is kind of hard without a picture) and the shared side, and they will have the ratio 1:sqrt(3), or 1/sqrt(3).

Set this equal to the base / 2 (remember that we cut the bottom in half) divided by x:

1/sqrt(3) = (b/2) / x

and solve for x:

x = (b/2)*sqrt(3).

If the explanation doesn't make sense, just use the formula for now. :)

Answer 2

An equilateral triangle has three equal sides and three equal angles. Therefore, each side is of length a and each angle is 60º. If you draw a line from the top angle straight down, you will have a right-triangle, where the length of the line you drew is the height.

Since the hypotenuse of the right triangle is a, and the bottom of the triangle is a/2 (because the line divides the bottom into two equal parts), the height is √(a^2-(a/2)^2)=√(3/4a^2)= √3a/2.

Therefore the height of an equilateral triangle with side length a is √3a/2=sqrt(3)a/2

Answer 3

An equilateral triangle has 60 degree angles. If you split it in half, you get a 30-60-90 triangle, which is a right triangle. Then you can use a^2+b^2=c^2 to determine the height.

Answer 4

1/2*b*h is the equation for a right triangle. If you cut the base in half you get a right triangle. The height is the same.

Answer 5

pythagorean theorum. If you cut the triangle in half, you create a 90 degree angle. The length of one side, and the lenght of half the other side are given. You have to find the third. A^2+B^2=C^2

Answer 6

height = Roof 2[side^2 + bottom ^ 2]

Answer 7

1/2*Base*height = area.
Therefore, height = (area*2)/base

Answer 8

Given the side s,

h = sqr(s^2 - (s/2)^2)

h = sqr(s^2 - s^2/4)

h = s x sqr(3)/2

Answer 9

let r be the side then take square root of 3/4 &multiply it with r.

Answer 10

a+b=c