What is the height of an equilateral triangle that has sides of length 1 cm?

if you bisect one of the angles, you have a right triangle with a hypotenuse of 1 cm and a short leg of 0.5 cm. Using the Pythagorean theorem, the height would be:

height = square root (1^2 - 0.5^2)

To find the height of an equilateral triangle with sides of length 1 cm, we can use the formula for the height of an equilateral triangle:

height = (√3 / 2) * side length

Substituting the side length of 1 cm into the formula:

height = (√3 / 2) * 1 cm

Calculating the value:

height = (√3 / 2) cm

Therefore, the height of an equilateral triangle with sides of length 1 cm is (√3 / 2) cm.

To find the height of an equilateral triangle, we can use the Pythagorean theorem.

An equilateral triangle has all three sides equal in length. In this case, the length of each side is given as 1 cm.

To find the height, we can draw a perpendicular line from one of the vertices of the triangle to the midpoint of the opposite side. This line represents the height.

Since the triangle is equilateral, the perpendicular line bisects the base, creating two congruent right triangles. Let's call the height h and the base (side length) b.

Now, we have a right triangle with one leg of length b/2 and a hypotenuse of length b. Using the Pythagorean theorem, we can calculate the height.

According to the Pythagorean theorem:
(h)^2 + (b/2)^2 = b^2

Simplifying this equation, we get:
h^2 + (b^2)/4 = b^2

Multiplying both sides of the equation by 4, we get:
4h^2 + b^2 = 4b^2

Subtracting b^2 from both sides, we get:
4h^2 = 3b^2

Dividing both sides of the equation by 4, we get:
h^2 = (3/4)*b^2

Taking the square root of both sides, we get:
h = sqrt((3/4)*b^2)

Since the length of each side in this equilateral triangle is 1 cm, we substitute b = 1 into the equation:
h = sqrt((3/4)*1^2)
h = sqrt((3/4)*1)
h = sqrt(3/4)
h = sqrt(3)/2

Therefore, the height of an equilateral triangle with sides of length 1 cm is (sqrt(3)/2) cm.

This wasn’t helpful if I’m in 6th grade