An equilateral triangle has sides of length 20. To the nearest tenth, what is the height of the equilateral triangle? Please explain what method you used.
+259 Since every side has the same length, u got in every of the 3. corners the same angle of 60.
Now if u split the equilateral triangle in the middle, u will get 2 halfs with each half having one angle of 90, one with 60(stays the same as unsplitted) and one with 30.
(sorry for that awful pic lol, but I just went for the first online draw thing on the internet)
So the middle line that splits the triangle is the heigh u want to calculate. Since u got a 90 angle by splitting it into 2 parts u can use the pythagoras to get the middle line.
a^2 + b^2 = c^2
b is what u want to have, so rearrange it to:
b^2 = c^2 - a^2
Length of c is the same as unsplitted of 20, a is the half since u splitted the down side into 2 halfs. so its 10
b^2 = 20^2 - 10^2
b^2 = 300. II ^(1/2) I cant use latex, so thats just taking the square root 2.
b = 17.3205080756887729
Also you can try to draw the graph to get the heigh, but it aint that accurate most times.
Area = Sqrt(3)/4 x S^2, S=Side
A =0.4330127 x 20^2
A =173.205 square units
173.205 =20 x H/2 divide both sides by 20
8.66025 =H/2 cross multiply
Height =17.3205 units.
+259 Since every side has the same length, u got in every of the 3. corners the same angle of 60.
Now if u split the equilateral triangle in the middle, u will get 2 halfs with each half having one angle of 90, one with 60(stays the same as unsplitted) and one with 30.
(sorry for that awful pic lol, but I just went for the first online draw thing on the internet)
So the middle line that splits the triangle is the heigh u want to calculate. Since u got a 90 angle by splitting it into 2 parts u can use the pythagoras to get the middle line.
a^2 + b^2 = c^2
b is what u want to have, so rearrange it to:
b^2 = c^2 - a^2
Length of c is the same as unsplitted of 20, a is the half since u splitted the down side into 2 halfs. so its 10
b^2 = 20^2 - 10^2
b^2 = 300. II ^(1/2) I cant use latex, so thats just taking the square root 2.
b = 17.3205080756887729
Also you can try to draw the graph to get the heigh, but it aint that accurate most times.
+36923 Another method: Using Amnesia's nice picture , you can see that the now divided triangle has angles of 30 60 90
Use law of sines sin60/b = sin 30/10 ('10' comes from dividing one '20' side in half = 10)
solve for b = 17.3205
