One side of an equilateral triangle measures 6 centimeters. Find the measure of an altitude of the triangle?

Answer 1

drop a line from the vertex to the bottom line of the triangle
you get a right angle triangle with side 6, 3 and x where x is the altitude of the triangle
6^2=3^2+x^2 use pythagoreus theorem
36=9+x^2
x=sqrt 27=3sqrt3=5.196cm

Answer 2

An "equilateral" triangle technique that each and every sides have the equivalent length. as a results of fact this additionally technique that all and sundry 3 corners have the comparable attitude you have 3 procedures to sparkling up it: One with Algebra and one with Trigonometry. For the two a form of you may desire to be looking at for the gap between any corner and the middle of the different section. you may desire to image this by using drawing the equilateral triangle with one corner pointing up, and drawing a line without delay down from that corner split it in to 2 smaller nicely suited triangles. you're looking at for the dimensions of that new line. Algebraic: Pythagorean Theorem says that a^2 + b^2 = c^2, the place a and b are the perimeters of a triangle and c is the hypotenuse (the long factor). which you would be waiting to organize this equation to therapy for any factor of a triangle, as long as you have the dimensions of two sides. as a results of fact all 3 sides of the basic triangle are the comparable length the long section your your 2 small triangles, or hypotenuse, are 6, and the gap from the middle of the nice and cozy button is a million/2 of 6, or 3. you presently would desire to organize the equation to sparkling up for the lacking leg, which we can call "a" a = ?(c^2 - b^2) (which will could learn as "a equals the oblong root of (c squared minus b squared)") Trigonometrical: If all 3 sides of a triangle are the comparable length then the angles of all 3 sides are equivalent: 360/3 or one hundred twenty. And all of us be responsive to the dimensions of each and every factor, 6. Having split the equilateral triangle in to 2 smaller good triangles we can call the recent factor we are looking at for opposite or "O" and the present longest section the Hypotenuse. The shortest leg, the backside, isn't needed for this answer. With this setup we can use the Sine of the corner attitude to furnish us the ratio of opposite over Hypotenuse, and multiply it by employing way of the dimensions of the hypotenuse to furnish us the dimensions of the different section, or the "altitude" of the equilateral triangle. O = Sin(one hundred twenty) * H

Answer 3

altitude of equilateral triangle=
( side ^2 - (1/2 x side) ^2 ) ^ 1/2

(6^2 - 3^2)^1/2 = (36 - 9) ^.5 = 5.19

Answer 4

in an eqilateral triangle,each angle is of 60 degree.
so if you draw an altitude that triangle breaks in two right triangle,
now hypo. is the side of given equilateral triangle,anle is 60 deg.
therefore,

sin60=alt/hypo

0.866 = alt. /6

alt = 0.866x6

alt=5.19

ans = 5.2cm

Answer 5

5.196 centimeters