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How do you calculate the length of a side of an equilateral triangle given the height?
Wiki User
∙ 15y ago
Letting S represent the length of a side of an equilateral triangle having a height of 1 unit, then drawing a perpendicular from the mid point of a side to the opposite vertex creates a right triangle having sides 1, S, and ½S, with S being the hypotenuse of a right triangle. The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides; thus S2 = (H2 + (½)2S2) = 1 + ¼S2. Subtracting 1 from each side, S2 - 1 = ¼S2. Multiplying the terms on each side by 4, 4S2 - 4 = S2; subtracting S2 from each side, 3S2 - 4 = 0; adding 4 to each side, 3S2 = 4; dividing each side by 3, S2 = 4/3; Taking the square root of each side, S = 2/1.732 = 1.1547 The length of each side of an equilateral triangle is the product of 1.1547 x height. (Note: 1.1547 is twice the reciprocal of the square root of 3.) Example: if the height of an equilateral triangle is 30 cm, the length of each side will be 34.641cm (30 x 1.1547cm).
Wiki User
∙ 15y ago
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What is the area of an equilateral triangle of side 2a?
The height of an equilateral triangle is √3/2 x side_length. So for an equilateral triangle of side length 2a, the area is: area = 1/2 x base x height 1/2 x (2a) x (√3/2 x 2a) = √3 a2
The length of an equilateral triangle is 66 what it the length of one side of the triangle?
10
What does equilateral triangle mean?
An equilateral triangle is one in which all three sides are of the same length.
What is the ratio of the length of a side of an equilateral triangle to its perimeter?
Length of a side of an equilateral triangle : Perimeter = 1 : 3 For example, if the length of the sides of an equilateral triangle were 5cm each, then perimeter would be three times that much - 15cm. 5 : 15 is the same as 1 : 3 when simplified. Length of a side of an equilateral triangle : Perimeter = 1 : 3 For example, if the length of the sides of an equilateral triangle were 5cm each, then perimeter would be three times that much - 15cm. 5 : 15 is the same as 1 : 3 when simplified.
What is the perimeter of an equilateral triangle with side length of 27cms?
27+27+27=81 The equation for the perimeter an equilateral triangle is "side + side + side". And since it is an equilateral all the sides are the same length.
How do you calculate height of a equilateral triangle?
square root (3) * side length / 2
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.
How do you find the height of an equilateral triangle if you have the length of the hypotenuse?
An equilateral triangle hasn't a hypotenuse; hypotenuse means the side opposite the right angle in a right triangle. An equilateral triangle has no right angles; rather all three of its angles measure 60 degrees. Knowing the length of the hypotenuse of a right triangle does not give enough information to determine the triangle's height. But the length of a side (which is the same for every side) of an equilateral triangle is enough information from which to calculate the height of that triangle. The first way is simply to use the formula that has been developed for this purpose: height = (length X sqrt(3)) / 2. But you can also use the geometry of right triangles to solve for the height. That is because you can bisect the triangle with a vertical line from the top vertex to the center of the base. The length of that line, which splits the equilateral triangle into two right triangles, is the height of the equilateral triangle. We know a lot about each right triangle formed by bisecting the equilateral triangle: * - The hypotenuse length is the length of the equilateral triangle's side. * - The base length is half the length of the hypotenuse. * - The angle opposite the hypotenuse is 90 degrees. * - The angle opposite the vertical is 60 degrees (the measure of every angle of any equilateral triangle). * - The angle opposite the base is 30 degrees (half of the bisected 60-degree angle). * - (Note that the sum of the angles does equal 180 degrees, as it must.) Now to solve for the height of a right triangle. There are a few ways. For labeling, let's let h=height of the equilateral triangle and the vertical side of the right triangle; A=every angle of the equilateral triangle (each 60o); s=side length of any side of the equilateral triangle and thus the hypotenuse of the right triangle. Since the sine of an angle of a right triangle is equal to the ratio of the opposite side divided by the hypotenuse, we can write that sin(A) = h/s. Solving for h, we get h=sin(A)/s. With trig tables you can now easily find the height.
What is the formula for the area for an equilateral triangle?
-- The area of any triangle is 1/2 (length of the base x height). -- For an equilateral triangle, that's equivalent to 1/2 x sqrt(3) x (length of a side).
What is the base and height of an equilateral triangle with an area of 12?
The base length is 5.2643 units and the height is 4.55902 units.
What is the area of an equilateral triangle with sides of ten inches and height of seven inches?
There is a problem with your question, namely that such a triangle does not exist. An equilateral triangle with sides of length 10 would have a height of 5 * (root 3), which is approx 8.66 (not 7 as the question states). An equilateral triangle of side length 10 inches would have an area of 25*(root 3), which is approx. 43.3 inches2.
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
A triangle with all sides the same length?
is called an equilateral triangle
How do you find the height of an equalateral triangle?
To find the altitude or height of an equilateral triangle, take one-half of the length of a side of the triangle and multiple by "square root" of 3. So, if for example, the side has length 10, the height = 5 Square root of 3.
Height of an equilateral triangle?
(1/2) square-root of (3) times the length of any side.
How do l work out the area of an equilateral triangle?
0.5 x base length x vertical height
Which triangle has the same length?
An equilateral triangle
