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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.
If the altitude of an equilateral triangle is 14 how long is each side of the triangle?
Each side of the triangle is 16.16581 units in length.
How do you calculate the height of an equilateral triangle given the lengths of all 3 sides?
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
Can the base and height of a triangle be perpendicular?
The base and height when calculating the area of a triangle are always perpendicular with each other.
The altitude of an equilateral triangle is 8cm . find the side?
The length of each side is 9.2376 cm. (rounded)
Find the area of each triangle?
Formula for area of Triangle: a=0.5(bh) Where b is the base length and h is the height. For example, a triangle of base 10 and height 5 has an area of 25.
How do you calculate perimeter of a triangle?
-- Measure or calculate the length of one side. -- Measure or calculate the length of another side. -- Measure or calculate the length of the only remaining side. -- Add the three numbers. The sum is the perimeter of the triangle. ----------------------------------- The perimeter is the sum of all three sides. Sometimes it is unnecessary to compute each side length; all we care about is the sum.
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.
Area of equilateral triangle?
To get the area of an equilateral triangle, you just need to know the length of one side. Multiply the length of one side by the square root of three and then divide the product by four, and you will get the area of the triangle.
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.
How do you calculate the length of a side of an equilateral triangle given the height?
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).
How do you work out the perimeter of a non right-angled triangle?
-- Measure or calculate the length of each of its 3 sides. -- Add the lengths of its 3 sides. -- The sum is the perimeter of the triangle.
How do you draw a triangle and a parallelogram that each have an area of 20 units?
Do you know the formula for the area of a triangle ? Pick a base-length and a height for your triangle so that 1/2 (base x height) = 20. Do you know the formula for the area of a parallelogram ? Pick a base-length and a height for your parallelogram so that (base x height) = 20. We're having a problem understanding your difficulty. Of course, if you don't know the formulas for area . . .
The perimeter of a triangle with equal sides is 36 miles what is the length of each side?
The length of each side of the triangle is 12 miles.
What are 2 and 3 dimensional figures?
A point is 0-dimensional ... it has no length, breadth or height. A line is 1-demensional ... it has length, but no breadth or height. A square, circle, triangle etc is 2-dimensional ... each of them have length and breadth, but no height A cube, cylinder, sphere etc is 3-dimensional ... each of them have lenght, breadth and height.
How is finding the area for a square and triangle alike?
-- For both shapes, multiply the length of the base by the height of the figure. -- For the triangle only, take 1/2 of the result. -- Now you have the area of each shape.
How do you find the length of a triangle when perimeter is given?
If the triangle is equilateral, you simply divide the perimeter by three to find the length of each side. If the triangle is not equilateral, you will need more information to determine the length of each side.
