Altitude question

[Guest]

The altitude of an equilateral triangle is 5.0cm. What is the length of a side? Please help.

 

[tkhunny]

An altitute of an Equilateral Triangle bisects the side it intersects.
An altitude intersects the side at a Right Angle.

Thus, If S = Length of a Side:

Altitude: 5.0 cm
Half-Length: S/2
Full Length: S

The Pythagorean Theorem

(5.0 cm)^2 + (S/2)^2 = S^2

Solve for S

 

[pka]

The length, h, of the altitude of an equilateral triangle with side s is \(\displaystyle \L
h = \frac{{s\sqrt 3 }}{2}\).

 

[Guest]

well since it's an equilateral triangle..
all the angesl are 60 degree
so if you draw an altitude
since the top angle is an angle bisector
it divides the angles into 30 degress each

Since altitude is "5"

___
X\/ 3 = 5
___
X = 5/ \/ 3
___
X = 5\/ 3 / 3

and that would be the half length of the base

what you do is since you have 2 trianges when you draw an altitude
and the opposite side of 60degree angles are always
__
" opposite the side of 30 degree angle [which at this time is a variable] * \/ 3 = altitude [or actually the opposite side of 60degree angle to be more acurate]"
but since you already have the altitude
all i did is reverse the equation
to solve the length of base

__
so when you get X = 5\/ 3 / 3
all you do is multiply that by the samething again
which becomes
__
X = 10\/ 3

Hope it helps, thx[/img][/code]

 

[Guest]

sry, that little _______ things
it was suppose to represent a square root
hope that clarifies a little