Each side of a equilateral triangle measures 12 cm. Find the height, h of the triangle.
Oh, the height of an equilateral triangle? That's easy peasy! Just like balancing on a tightrope while juggling bananas... ahem. Now, to find the height, h, of an equilateral triangle with side length 12 cm, we can use a little trick.
You see, in an equilateral triangle, the height bisects the base, splitting it right down the middle like a magician with a deck of cards. So, to find the height, we simply need to draw a straight line from any vertex (corner) of the triangle to the midpoint of the opposite side.
Now, this magical line, which we'll call the height, forms a right-angle triangle with the base. And since the base is divided into two equal halves, each measuring 6 cm, we now have a right-angle triangle with one side being 6 cm and the hypotenuse being 12 cm (the full side length of the equilateral triangle).
Using the Pythagorean theorem (which has been known to throw some interesting surprises), we can calculate the length of the height, h, as follows:
h² + 6² = 12²
h² + 36 = 144
h² = 108
h ≈ √108
h ≈ 10.39 cm
So, the height, h, of the equilateral triangle is approximately 10.39 cm. Now, go forth and conquer those geometry problems like a hilarious clown riding a unicycle!
To find the height (h) of an equilateral triangle, you can use the Pythagorean theorem.
Let's draw an equilateral triangle and label the sides.
Since all sides of an equilateral triangle are equal, each side measures 12 cm.
Now, consider the height (h) of the triangle. It is a perpendicular line segment drawn from one vertex to the midpoint of the opposite side. This segment divides the triangle into two right-angled triangles.
Let's label the midpoint of the base as M, and the vertex as A.
Since the triangle is equilateral, the height (h) bisects the base (segment MB), so MB is 6 cm.
Now, let's use the Pythagorean theorem to find the height (h).
In the right-angled triangle AMB, the hypotenuse is the side AM, and the other two sides are h (the height) and MB (6 cm).
According to the Pythagorean theorem, the square of the hypotenuse (AM) is equal to the sum of the squares of the other two sides.
So, we have:
AM^2 = h^2 + MB^2
Substituting the known values, we get:
AM^2 = h^2 + 6^2
AM^2 = h^2 + 36
Since all sides of the equilateral triangle are equal, AM is also 12 cm.
Substituting this value, we have:
12^2 = h^2 + 36
144 = h^2 + 36
Rearranging the equation, we get:
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we get:
h = √108
h ≈ 10.39 cm
Therefore, the height (h) of the equilateral triangle is approximately 10.39 cm.
To find the height, h, of an equilateral triangle, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In an equilateral triangle, the height (h) forms a right triangle with one of the sides as the base. The height, h, also bisects the base, creating two congruent right triangles.
Since all sides of an equilateral triangle are equal, each side measures 12 cm. And since the triangle is equilateral, the base also measures 12 cm.
Let's consider the right triangle formed by the height (h), the base (12 cm), and the hypotenuse (the side of the equilateral triangle).
Using the Pythagorean theorem:
(base)^2 + (height)^2 = (hypotenuse)^2
Substituting the known values:
(12 cm)^2 + (h)^2 = (hypotenuse)^2
Now, we need to find the hypotenuse. In an equilateral triangle, each side is equal, so the hypotenuse is also 12 cm.
(12 cm)^2 + (h)^2 = (12 cm)^2
Simplifying the equation:
144 cm^2 + (h)^2 = 144 cm^2
Since both sides of the equation are equal, the two terms on each side must be equal as well:
(h)^2 = 0 cm^2
This implies that h = 0 cm.
Therefore, the height of the equilateral triangle is 0 cm.
Note: It is important to double-check the given measurements and calculations to ensure accuracy.
The height(altitude) divides the triangle into two congruent rt. triangles:
X = 12cm/2 = 6cm = Hor. side.
Y = h = Ver. side.
Z = 12 cm = Hyp.
Y = Z*sin60 = 12*sin60 = 10.4 cm. = Ht.