What is the formula to determine the median of an equilateral triangle?
In an equilateral triangle, the median is the same as the altitude. If the side is s, the median is √3/2 s. Each median extends from a vertex to the midpoint of the opposite side.
Not geography or geothermal science or ...
The median of an equilateral triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. The formula to determine the length of the median is:
Median length = (√3/2) * side length
where the side length represents the length of one side of the equilateral triangle.
To determine the median of an equilateral triangle, you can use a simple formula:
Median = (1/2) * height
In an equilateral triangle, the height is the line segment drawn from any vertex perpendicular to the opposite side.
To find the median, you need to know the height of the equilateral triangle. The height can be calculated using the Pythagorean theorem or trigonometric functions.
1. Using the Pythagorean theorem:
- Divide the equilateral triangle into two congruent right triangles by drawing the median from any vertex to the midpoint of the opposite side.
- Let's assume one side of the equilateral triangle is "s". The height of the equilateral triangle can be found by calculating h = √(s^2 - (s/2)^2).
- Once you have obtained the height, use the formula mentioned earlier to find the median: Median = (1/2) * height.
2. Using trigonometric functions:
- Divide the equilateral triangle into two congruent right triangles by drawing the median from any vertex to the midpoint of the opposite side.
- In an equilateral triangle, the angles are all 60 degrees.
- Let's assume one side of the equilateral triangle is "s". The height of the equilateral triangle can be calculated using the formula h = s * sin(60°).
- Once you have obtained the height, use the formula mentioned earlier to find the median: Median = (1/2) * height.
By applying either of these methods, you can determine the median of an equilateral triangle.