Equilateral triangle?

Question

An equilateral triangle has a perpendicular height of 12m. Calculate the length of the sides of the triangle. (corr. to 2 dp)

How on earth do u do this???? Pythagoras's theorem is confusing me!

Answer 1

i think we might be better off to use sin cos or tan for this one....





soh cah toa

(where x = one of the non 90 degree angles)



soh....Sin(x) = Opposite side / Hypotenuse

cah....Cos(x) = Adjacent side / Hypotenuse

toa.....Tan(x) = Opposite side / Adjacent side





the top angle of your (half triangle) is 30, and the bottom is 60



lets us cah



cos30 = 12 / h

h = 12 / cos30

h = 12 / .866

h = 13.86



lets check this against pythagorean....



lets call your base to be 1/2 of 13.86

so...



12^2 + 6.93^2 = 13.86^2

144 + 48.029 = 192.0996, close enough



NOTE: BluLuKa, your equation is faulty there....you have named your hypotenuse to be 12, 12 is one of the legs



should be more like this....



a^2 + b^2 = (2b)^2

12^2 = (2b)^2 - b^2

....complicated

Answer 2

An isosceles triangle is any triangle with 2 aspects that are equivalent in length. So each and every equilateral triangle is a particular case of an isosceles triangle considering that not basically 2 aspects are equivalent, yet all 3 are. yet each and every isosceles triangle isn't equilateral, considering which you are able to have 2 aspects of equivalent length and a third component that's the two longer or shorter than those 2 aspects. as an occasion, if the triangle is a real-perspective triangle and the two aspects that meet to make the the best decision perspective are the comparable length, then the third component could be longer than those 2. desire that enables.

Answer 3

The definition of an equilateral triangle is that all sides are of equal length.

The perpendicular height divides the base in half forming two right triangles. The base is now equal to 1/2 of one of the sides. In this case, the longer side is the hypotenuse and equal to "c" in the Pythagorium theorem.



Using the Pythagorium theorem

c^2 = a^2 + b^2

a^2 = c^2 - b^2

c = hypotenuse

b = base of the right triangle

a = height of 12m

c = 2b

12^2 = (2b)^2 - b^2

12^2 = 4b^2 - b^2

144 = 3b^2

b^2 = 144/3

b^2 = 48

c^2 = 144 + 48 = 192

c = 13.86

So all sides are approximately equal to 13.86m each.



Proof

c^2 = a^2 + b^2

13.86^2 = 12^2 + 48

192 = 144 + 48

Answer 4

a^2+b^2=c^2



a=length of one side of the triangle

b=length of another side of the triangle

c=the height of the triangle

a=b since its an equilateral triangle



a^2+b^2=c^2

b^2+1/2b^2=12^2

1.5b^2=144

b^2=144/1.5

b^2=96

b=the square root of 96





sry but idk if this rite