Question 467362: Could you please help me with this question?
"An equilateral triangle has a height of 10 inches. How long are it's sides?"
Thanks so much! Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! equilateral triangle has 3 sides of equal length.
the height is equal to 10.
the height drops from one of the vertices and is the perpendicular bisector of the opposite side.
it divides the equilateral triangle into 2 right triangles that have a 90 degree angle and a 60 degree angle and a 30 degree angle.
a 30 / 60 / 90 degree triangle has the following properties:
sine (30) = 1/2
sine (60) = sqrt(3)/2
we can use either the 60 degree angle or the 30 degree angle to find the length of the hypotenuse of one of these triangle.
that hypotenuse is one of the sides of the equilateral triangle which becomes the length of each of the sides of the equilateral triangle.
since the height of our triangle is 10 and this is opposite the 60 degree angle, we'll use sine (60) = 10 / hypotenuse.
we'll solve for hypotenuse to get hypotenuse = 10 / sine (60)
this becomes 10 / ((sqrt (3) / 2) which becomes 20 / sqrt(3) which becomes 11.54700538 inches.
each side of your equilateral triangle is equal to 11.54700538 inches.
shown below is a picture of your triangle:
