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How do you find the height of an equilateral triangle if you have the length of the hypotenuse?
Wiki User
∙ 15y ago
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.
Wiki User
∙ 15y ago
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What is the length of the hypotenuse of a right triangle with a 13 centimeters base and a 6 centimeters height?
The length of the hypotenuse of a right triangle with a 13 cm base and a 6 cm height is 14.32 cm
What is the length of the hypotenuse of a right triangle that has a base of 3 feet and a height of 12 feet?
The length of the hypotenuse of a right triangle that has a base of 3 feet and a height of 12 feet is: 12.37 feet.
What is the length of the altitude of an equilateral triangle whose side has a length of four?
The altitude/height of an equilateral triangle can be calculated by taking the perpendicular bisector of any side. This line will bisect its opposite angle forming two congruent right angled triangles. The side length of the original equilateral triangle is the hypotenuse and the short leg of right angled triangle is half the hypotenuse. By Pythagoras' Theorem : 42 = 22 + L2.........where L is the length of the altitude. L2 = 42 - 22 = 16 - 4 = 12 L = √12 = 2√3 = 3.464 (3dp)
What is the length of the median to the hypotenuse of a right triangle if the hypotenuse is 12 inches in length?
The median to the hypotenuse of a right triangle that is 12 inches in length is 6 inches.
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.
How can you find the base of a right triangle when you have the height and hypotenuse?
The square of the length of the base plus the square of the length of the height will equal the square of the length of the hypotenuse of your right triangle, per Pythagoras. Square the hypotenuse, subtract the square of the height, and then find the positive square root of that and you'll have the base of your right triangle.
What is the length of the hypotenuse of a right triangle with a 13 centimeters base and a 6 centimeters height?
The length of the hypotenuse of a right triangle with a 13 cm base and a 6 cm height is 14.32 cm
What is the length of the hypotenuse of a right triangle that has a base of 3 feet and a height of 12 feet?
The length of the hypotenuse of a right triangle that has a base of 3 feet and a height of 12 feet is: 12.37 feet.
What is the length of the altitude of an equilateral triangle whose side has a length of four?
The altitude/height of an equilateral triangle can be calculated by taking the perpendicular bisector of any side. This line will bisect its opposite angle forming two congruent right angled triangles. The side length of the original equilateral triangle is the hypotenuse and the short leg of right angled triangle is half the hypotenuse. By Pythagoras' Theorem : 42 = 22 + L2.........where L is the length of the altitude. L2 = 42 - 22 = 16 - 4 = 12 L = √12 = 2√3 = 3.464 (3dp)
The ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?
Starting with an equilateral triangle of side 2, dropping a perpendicular from one vertex to the opposite base creates two equal right angled triangles with hypotenuse of length 2, base length 1 and height of length √(22 - 12) = √3 which is the longer leg of the 30-60-90 triangle. Thus the ratio of longer_leg : hypotenuse is √3 : 2
What is pythagarous theorm?
That for any right angle triangle the length of its hypotenuse when squared is equal to the of length of the base when squared plus the length of the height when squared:- a2+b2 = c2 where a and b are the base and the height of the triangle and c is its hypotenuse.
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 length of the hypotenuse of a right triangle that has a base of 10 feet and a height of 10 feet?
The hypotenuse is 14.14 feet.
How do you calculate height of a equilateral triangle?
square root (3) * side length / 2
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.
Is a hypotenuse equal to the sides of an equalateral triangle?
Yes. The equilateral triangle will have all sides with the same length. An equilateral triangle will ALSO be a equiangular, with each angle being 60 degrees. This fact does not extend to other polygons. An equilateral quadrilateral is a rhombus, while an equiangular quadrilateral is a square.
