what is the altitude of an equilateral triangle whose side is "s"?

Answer 1

mmmm....check a globe

Answer 2

You should remember your 30-60-90 triangles... Any equilateral can be split into 2 30-60-90 triangles. One of thir sides is the altitude, the other is a side, and the last is half a side. So, using the pythagorean theorem,
altitude^2 + (s/2)^2 = s^2
altitude^2 = s^2 - s^2/4 = 3s^2/4
altitude = s*sqrt(3)/2

Answer 3

OK, pick a side. You'll notice that the altitude will go from the center of that side up to the corner. AH, now we have a right triangle. The hypotenuse has length s, and the one leg (the shorter one, by the way) has length s/2.

s^2 = (s/2)^2 + a^2 for a our altitude.

SO! a^2 = s^2 * (1-1/4)

OR, a = sqrt(3)*s/2 for sqrt the square root function

That means a = ~ 0.866*s give or take a bit

Answer 4

let altitude be X. Since it is an equilateral triangle all sides are equal = S. Hence Hypotenuse = S, Base = S/2. ( Because altitude of an equilateral triangle divides base equally)

Now use the formula which I am sure you know ...

hypotenuse square = altitude square + base square

Answer 5

Easy. Draw a line down from the vertex, perpendicular to the base. you have formed 2 triangles with a base of 8cm and a hypoteneuse of 16cm. 16 square minus 8 square will equal the altitude squared. 256-64 = 192 answer:square root of 192

Answer 6

If you have to calculate the area of a triangle and are not given the height to use the traditional formula 1/2bh, you can determine the height by the formula by knowing the angle of the base (being equilateral, that is a known 60degrees) valued as "B",

Find the sine of B, is equal to the side divided by the height.
sinB=s/h or h=s/sinB

Just takes a little trigonometry. :-)

Answer 7

let altitude be x units. for equilateral triangle altitude is also median. thus it divides its base in half.thus length of half base is s/2 units. by applying pythagoras theorem to triangle formed by altitude on either its right or left side, equation is:
(s)square=(s/2)square + (x)square
solving, u get x=1.73s/2

Answer 8

It will be
1/2*square root of 3*S
fore example if sides are =4,
then altitude will be square root of 12
(use Pythagoras theorem)

Answer 9

it is by using the Great Pythagorus theorem.
let a be altiitude then,
s*s = (s/2)*(s/2) + a*a
solvin this u will get the answer.
a=sqrt(3)/2 times s

Answer 10

the height of an eq triangle is s/2 x radical3

Answer 11

h = (s * sqrt(3))/2