Find the height of an equilateral triangle with sides of length 6 cm ' please show ur work
Let the side length of the equilateral triangle be L. Bisect one angle of the equilateral triangle and let the bisector intersect the opposite side, in the middle. You will have split the original triangle into two 30-60-90 right triangles. The side lengths will be L, L/2 and L*sqrt3/2 for those triangles.
The last of those is the height of the original equilateral triangle.
height = 3 sqrt2 = 4.24264 cm
Thank you :D
To find the height of an equilateral triangle, you can use the Pythagorean theorem or trigonometric functions. I will explain both methods.
Method 1: Using the Pythagorean theorem.
1. Draw the equilateral triangle with side length 6 cm.
2. Draw a perpendicular line from one of the vertices of the triangle to the opposite side, forming two right-angled triangles.
3. The line you drew is the height of the equilateral triangle, which we will denote as 'h'.
4. Since the equilateral triangle has all sides equal, the base of the right-angled triangle is half of the side length, which is 6/2 = 3 cm.
5. The hypotenuse of the right-angled triangle is the side length of the equilateral triangle, which is 6 cm.
6. Apply the Pythagorean theorem: h^2 = (6 cm)^2 - (3 cm)^2
h^2 = 36 cm^2 - 9 cm^2
h^2 = 27 cm^2
7. Take the square root of both sides to find 'h':
h = √(27 cm^2)
h ≈ 5.2 cm
Therefore, the height of the equilateral triangle with sides of length 6 cm is approximately 5.2 cm.
Method 2: Using trigonometric functions.
1. In an equilateral triangle, all angles are 60 degrees.
2. Draw the equilateral triangle with side length 6 cm.
3. Draw a line segment from one of the vertices to the midpoint of the opposite side, creating a right-angled triangle.
4. The height of the equilateral triangle is the longer side of the right-angled triangle, which we will denote as 'h'.
5. The base of the right-angled triangle is half of the side length, which is 6/2 = 3 cm.
6. Since the angle opposite to the height is 60 degrees, we can use the trigonometric ratio: tan(60°) = h / 3.
7. Solve for 'h': h = 3 * tan(60°)
h ≈ 3 * 1.732
h ≈ 5.2 cm
Again, the height of the equilateral triangle with sides of length 6 cm is approximately 5.2 cm.