Each side of a equilateral triaganl measures 12 cm find the high , h of the triangle
The height of an equilateral triangle can be found using the Pythagorean theorem.
Let h represent the height of the triangle. We can divide the equilateral triangle into two right triangles by drawing a line from one of the vertices to the center of the opposite side.
The base of one of the right triangles is half of the length of one side of the equilateral triangle, which is 6 cm. The hypotenuse of the right triangle is the side of the equilateral triangle, which is 12 cm.
Using the Pythagorean theorem, we can find the height (h) of the right triangle:
h^2 = 12^2 - 6^2
h^2 = 144 - 36
h^2 = 108
h = √108
h ≈ 10.39 cm
Therefore, the height of the equilateral triangle is approximately 10.39 cm.
To find the height (h) of an equilateral triangle, we can use the formula:
h = (√3/2) * s
where s is the side length of the equilateral triangle.
In this case, the side length (s) is given as 12 cm. Let's substitute this value into the formula:
h = (√3/2) * 12
Next, we can simplify the expression:
h = (√3/2) * 12
h = (√3 * 12)/2
h = (√36 * √3)/2
√36 is equal to 6, so we can substitute this into the equation:
h = (6 * √3)/2
Lastly, we can simplify the expression further:
h = 6/2 * √3
h = 3 * √3
Therefore, the height (h) of the equilateral triangle is 3√3 cm.
To find the height (h) of an equilateral triangle, you can use a trigonometric relationship involving the side length of the triangle.
In an equilateral triangle, the height (h) forms a right triangle with one side of the triangle as the base and the height as the hypotenuse.
Since the triangle is equilateral, all sides are equal, so each side of the triangle is 12 cm. The base of the right triangle is half of one side, which is 12/2 = 6 cm.
To find the height (h), we need to find the length of the hypotenuse. Using the Pythagorean theorem, we have:
h^2 = (side length)^2 - (base length)^2
h^2 = 12^2 - 6^2
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we get:
h = √108
Simplifying the square root of 108, we have:
h ≈ 10.39 cm
Therefore, the height (h) of the equilateral triangle is approximately 10.39 cm.