Triangle median calculator

The median of a triangle is the line connecting the top of the triangle to the middle of the opposite side. The triangle has three sides; therefore, three medians can be constructed. All medians intersect at one point.

Triangle — is a geometric figure that has three points that do not lie on the same line and three segments that pair these points in pairs. The points of a triangle are usually called its vertices, and the segments are called its sides.

Our triangle median calculator makes it easy for you to find the medians of your triangle. Simply chose the type of your triangle enter the required values of the triangle into the calculator, and it will automatically calculate the medians for you. This tool is perfect for students, teachers, and anyone else who needs to calculate triangle medians quickly and accurately.

Triangle Median Formula

There are several formulas that you can use to calculate the length of a median of a triangle.

Through sides

The median of the triangle emerges from the corner and divides the opposite side in half. You can find the median in an arbitrary triangle using Stewart's theorem. Stewart's theorem states that if there is a point A on the side of the triangle connected to an angle opposite to that side, then there is a ratio of all three sides of the triangle, in which it becomes possible to find not only the parts into which point A divided the above side, but also a segment, connecting point A with the angle of the triangle. The formula is:

m_a = \dfrac{1}{2}\sqrt{2c^2 + 2b^2 -a^2}m_b = \dfrac{1}{2}\sqrt{2c^2 + 2a^2 -b^2}m_c = \dfrac{1}{2}\sqrt{2a^2 + 2b^2 -c^2}

Where a, b, c are triangle sides and m_a, m_b and m_c are the medians of the triangle respectively.

Right triangle, through sides

The median of a right triangle dividing the hypotenuse in half is equal to the resulting halves of the hypotenuse. Thus, the median divides the right triangle into two isosceles triangles with legs in the form of bases. In order to calculate the median of a right triangle, it is enough to know the hypotenuse, two legs, or one leg and the angle in the triangle. The formula is:

m = \dfrac{1}{2}\sqrt{a^2+c^2}

Where a, c are the legs of the right triangle.

Isosceles triangle, through side and angle

The median of an isosceles triangle, lowered to the base, coincides with the height and bisector drawn from the same angle. Therefore, in order to calculate the median in an isosceles triangle, we use the height formula and multiply the side of the triangle by the sine of the angle at the base. The formula is:

m = h = asin(\alpha)

Equilateral triangle, through side

In an equilateral triangle, the medians, as well as in the isosceles median of the base, are equal to each other and coincide with the bisectors and heights. Using this property, we find the median of an equilateral triangle as height. To do this, we turn to a right triangle, in which the median is a leg, and the side of the triangle is a hypotenuse. The formula is:

m = h = \dfrac{\sqrt{3}}{2}a

Where h is the height of the triangle.

Example

Let's say we have a triangle with sides a = 6, b = 8, and c = 10. To find the medians, we can use the formulas above:

• Median to side a:m_a = \dfrac{\sqrt{2*8^2 + 2*10^2 -6^2}}{2} = \sqrt{116} ≈ 10.77
• Median to side b:m_b = \dfrac{\sqrt{2*6^2 + 2*10^2 -8^2}}{2} = \sqrt{96} ≈ 9.8
• Median to side c:m_c = \dfrac{1}{2}\sqrt{2*6^2 + 2*8^2 -10^2} = \sqrt{84} ≈ 9.17

Conclusion

In conclusion, the triangle median is an important concept in geometry that is used to find the centroid and calculate the area of a triangle. Our triangle median calculator makes it easy for you to find the medians of your triangle quickly and accurately. Whether you are a student, teacher, or anyone else who needs to calculate triangle medians, our calculator will help you get the job done.