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How do you calculate the height of an equilateral triangle given the lengths of all 3 sides?
Wiki User
∙ 12y ago
Half the length of one side multiplied by (square root of 3)/(2).
in triangle ABC with height H:
(A•sqrt3)/2 or A (sqrt3)/2
This is because of the Pythagorean theorem.
You draw a line from the top vertex of the triangle vertically to the bottom side. This line is perpendicular to the bottom side and it will bisect that side. Now you want to know the length of your new line. On each side of it, you have a smaller triangle, one side with the length of the side of the original triangle (let's call it s) and one side with length half that, (1/2)s. Since the side with length s will be the hypotenuse of the triangle, we know s2 = (s/2)2 + h2 by the Pythagorean theorem. (h stands for height.)
s2 = s2/4 + h2
s2 (1-1/4) =h2
s2(3/4) =h2
(sqrt3)s/2 = h
Wiki User
∙ 12y ago
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What is the height of an equilateral triangle with a length of x?
Cutting the equilateral triangle in half results in two right triangles each with a base of length x/2, and angles of 30, 60, and 90 degrees. Using the lengths of sides of a 30-60-90 triangle it can be found that the height is (x/2)√(3), which is the same as the height of the equilateral triangle.So the height of the equilateral triangle is x√(3) / 2.
Does 5cm 5cm 5cm make a triangle?
5cm, 5cm, and 5cm could represent the lengths of the sides of an equilateral triangle, or might indicate the length, width, and height of a cube.
How do you find the perimeter of a triangle with perpendicular height?
The height of a triangle alone is not enough information to find the perimeter. You need some angle measures or side lengths.
If the side length of an equilateral triangle is 5 centimeters what is the length of the altitude of the triangle?
Height = sqrt(3)/2 * length of side So here, approx 4.3301 cm
How do you calculate the height of right triangle given the base and adjacent angle?
Height will be h=base*tan(angle).
Is the height of an equilateral triangle the same as the side lengths?
No. 1/2 base squared + height squared=side squared on an equilateral triangle.
What is the height of an equilateral triangle with a length of x?
Cutting the equilateral triangle in half results in two right triangles each with a base of length x/2, and angles of 30, 60, and 90 degrees. Using the lengths of sides of a 30-60-90 triangle it can be found that the height is (x/2)√(3), which is the same as the height of the equilateral triangle.So the height of the equilateral triangle is x√(3) / 2.
What is the height of an equilateral triangle with the side lengths of 18 center meters?
In effect an equilateral triangle is made up of two right angle triangles joined together so use Pythagoras' theorem to find the height:- 182-92 = 243 and the square root of this will be the height of the equilateral triangle which is about 15.588 cm
How do you calculate the area of an equilateral triangle?
Area = 1/2*base*perpendicular height.
How do you calculate height of a equilateral triangle?
square root (3) * side length / 2
How do you find the side lengths of an equilateral triangle if all you know is the height?
you times the length by the amount of sides then you divide the answer by 100
Does 5cm 5cm 5cm make a triangle?
5cm, 5cm, and 5cm could represent the lengths of the sides of an equilateral triangle, or might indicate the length, width, and height of a cube.
An equilateral triangle has an area of What is the height?
8.7
What is the area of equilateral triangle with height is 20 and Base is 15?
An equilateral triangle with a height of 20 has a base of 23.1 (23.09401), not 15. If the base is 15 then the height will be 13 (12.99038).
If each side of the equilateral triangle measures 9c find the height of the triangle?
The area of a triangle is one-half the product of the triangle's base and height. The height of an equilateral triangle is the distance from one vertex along the perpendicular bisector line of the opposite side. This line divides the equilateral triangle into two right triangles, each with a hypotenuse of 9c and a base of (9/2)c. From the Pythagorean theorem, the height must be the square root of {(9c)2 - [(9/2)c]}, and this height is the same as that of the equilateral triangle.
What is the height of an equilateral triangle with the side lengths of 8 inches?
Equilateral triangle means that all sides are equal in length. When it is asked for a height of equilateral triangle it refers to vertical distance from highest point of the triangle to the lowest(Right in the middle). So we got two known and one unknown which tells us that we can use Pythagorean Theorem C2=A2 + B2 A=4 B=? C=8 Solve for B and you will get answer Square root of 48.
The height of an equilateral triangle is 6cm.find the area?
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