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How do you construct a triangle when all the three length of median are known?
Wiki User
∙ 14y ago
By using Apollonius' theorem, the length of the median of a triangle of sides of length a, b, c is given by:
ma = sqrt( (2b2 + 2c2 - a2) / 4)
where ma is the median that meets the midpoint of a; and similarly for mb and mc. By rearranging this, the sides (a, b, c) of a triangle can be obtained from the lengths of the medians (ma, mb, mc):
a = 2/3 sqrt(2mb2 + 2mc2 - ma2)
b = 2/3 sqrt(2mc2 + 2ma2 - mb2)
c = 2/3 sqrt(2ma2 + 2mb2 - mc2)
Once the sides are known (using the above), the triangle can be drawn fairly easily using a ruler and compasses.
Wiki User
∙ 14y ago
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Perimeter of a triangle with base length and height length known?
Is indeterminate.
How do you know when a triangle is 90 degrees?
we know that a triangle is 90 degrees by measuring its length or it can be known as right triangle which measures 90 degrees.
Is 10 a right triangle?
If the length of only one side is known, it is not possible to determine whether or not the triangle is right angled.
What is an ambiguous triangle?
The answer may refer to a triangle for which the length of two sides and the measure of an angle - other than the included angle - are known.
How would you construct a trapezoid given the length of the top and the bottom and the length of BOTH diagonals?
Consider the trapezium ABCD in which AD and BC are the top and the bottom - parallel and of known length - and AC and BD are the diagonals - also of known length. Suppose AC and BD intersect at O. Then, it can be shown that triangles AOD and COB are similar. Therefore AO/OC = DO/OB = AD/BC where both lengths for the last ratio are known. Then, given AC, it is possible to calculate OC (and AO) and given BD, it is possible to calculate OB (and DO). So all sides of triangle COB are known and so it is easy to construct it. Then simply extend BO to D (adding OD) and CO to A (adding OA). Join BA, AD and DC. Done!
Concurreny of medians of triangle?
The three medians are concurrent at a point known as the triangle's centroid. This is the center of mass of the triangle. Two-thirds of the length of each median is between the vertex and the centroid, while one-third is between the centroid and the midpoint of the opposite side.
Perimeter of a triangle with base length and height length known?
Is indeterminate.
What formula do you use to find the median in an isosceles triangle?
It is not possible to answer the question since it is hopelessly underspecified and does not provide enough information.what information about the triangle is known? All three side lengths, base angle and base side, base angle and leg, apex angle and base, apex angle and leg? These could influence the form of the answer.is the information about the triangle in terms of analytical geometry (coordinates of points and equations of lines) or in some other form?which median? The median from the apex or one of the isosceles medians?what aspect of the median is the formula supposed to give? Its length, equation?
How do you know when a triangle is 90 degrees?
we know that a triangle is 90 degrees by measuring its length or it can be known as right triangle which measures 90 degrees.
Is 5 a right triangle?
If the length of only one side is known, it is not possible to determine whether or not the triangle is right angled.
Is 10 a right triangle?
If the length of only one side is known, it is not possible to determine whether or not the triangle is right angled.
What is an ambiguous triangle?
The answer may refer to a triangle for which the length of two sides and the measure of an angle - other than the included angle - are known.
How would you construct a trapezoid given the length of the top and the bottom and the length of BOTH diagonals?
Consider the trapezium ABCD in which AD and BC are the top and the bottom - parallel and of known length - and AC and BD are the diagonals - also of known length. Suppose AC and BD intersect at O. Then, it can be shown that triangles AOD and COB are similar. Therefore AO/OC = DO/OB = AD/BC where both lengths for the last ratio are known. Then, given AC, it is possible to calculate OC (and AO) and given BD, it is possible to calculate OB (and DO). So all sides of triangle COB are known and so it is easy to construct it. Then simply extend BO to D (adding OD) and CO to A (adding OA). Join BA, AD and DC. Done!
What can you say about the sides of a triangle opposite the largest angle?
The side of a triangle opposite the largest angle is the side of greatest length. It is also known as the Hypotenuse.
Is an isosceles triangle considered a regular triangle?
An isosceles triangle is not a regular triangle because it has 1 side that doesn't equal the other 2. For it to be a regular triangle it will need to have all sides the same length. Here are the three types of triangle classification: In a equilateral triangle or also known as regular triangle "all" sides must have the same length. In an isosceles triangle "at least" two sides must have the same length. In an scalene triangle all sides must be of different lengths Therefor it can be said that a regular triangle is a type of isosceles triangle since it has at least 2 sides of the same length. But remember if one side changes length and 2 remain the same it becomes an isosceles, if all sides are of different lengths then it becomes scalene.
What is the formula for finding the length of the hypotenuse of a right triangle?
The forumal for finding the finding the length of the hypotenuse of a right triangle is square root of a squared plus b squared equals c. The letters a and b are the two sides that the length is known and the c is the unknown side.
What is known as In a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs?
Pythagorean Theorem
