find the altitude of an equilateral triangle if a side is 6 mm long.
Use the Pythagorean Theorem.
http://mathcentral.uregina.ca/QQ/database/QQ.09.02/rosa2.html
To find the altitude of an equilateral triangle with a side length of 6 mm, we can use the following steps:
1. Start by drawing the equilateral triangle with a side length of 6 mm.
2. Draw a line segment from one of the vertices of the triangle to the opposite side, forming a right angle with the side.
3. This line segment is the altitude of the equilateral triangle.
4. To find the length of the altitude, we need to calculate the height of the right-angled triangle formed by the altitude.
5. Since the equilateral triangle is made up of two congruent 30-60-90 right-angled triangles, we can use the properties of this special triangle to find the height.
6. In a 30-60-90 triangle, the ratio of the side lengths is 1:√3:2. The side opposite the 30-degree angle is half the length of the hypotenuse.
7. In our case, the side opposite the 30-degree angle is the height we are looking for, and the hypotenuse is the side length of the equilateral triangle (6 mm).
8. Applying the ratio, we know that the height is half the side length multiplied by √3.
9. Therefore, the altitude of the equilateral triangle is (6 mm/2) * √3, which simplifies to 3√3 mm.
So, the altitude of the equilateral triangle with a side length of 6 mm is approximately 3√3 mm.