How to calculate the height of an equilateral triangle? There are different ways to know how to calculate the height of an equilateral triangle: using the Pythagorean Theorem, using trigonometry, the area formula, or the specific formula h = x√3 / 2, where H’ is height and X’ is a triangle. See step by step.
Introduction to the equilateral triangle: useful features!
The equilateral triangle is the favorite of two Geometry students. It is the easiest of all! It is because distribution or reasoning makes life easier for us. But this only happens when we understand its characteristics. Now you need to know the essential features that we have because we will use them more for the front:
- Equal sides:
A proper equilateral word tells us about this property: “equi = equal” and “lateral = side”
In this way, it is made to measure on two sides. We know that all the others are the same.
- Equal angles:
It does not matter what you choose or the size of the equilateral triangle. You will use a transfer or (angle measure). You will always find the same value for all your angles!
This happens for a reason: so that all equal sides meet in a perfect triangle format. Two sides will always form the same angle with each other. And this leads us to another discovery! We know that the sum of two interior angles in any triangle is 180. Therefore, if not equilateral, everything is equal. We can do 180/3 = 60.
- Equal heights:
Guess! We know all the sides and angles are the same. It doesn’t matter from which side you draw the height. Agree? Then they will always be the same!
Pythagorean Theorem and height of the equilateral triangle
Now that we have learned everything or what is essential, we can start talking about how to discover the height of the equilateral triangle. Height is a grid segment that forms a sharp angle (90) with the surface.
What is the Pythagorean Theorem?
In mathematics, the Theorem means a formula always applied in a specific situation. Not in the case of Pythagoras. It should be used only in right triangles (the one in which two angles should be 90 degrees).
As a mathematician, we came to this conclusion, and it is not our focus here. But, to continue, we need to know what he said:
“A sum of two legs to a square is equal to the hypotenuse value to a square.”
The hypotenuse is the opposite side of the right angle, or the longest side of a right triangle. The legs are the remaining sides, the sides adjacent to the challenge angle.
How to calculate the height of an equilateral triangle using Pythagoras?
To know how to calculate the height of an equilateral triangle, we need to use the Pythagorean Theorem. See or step by step:
- We must trace at the height of the equilateral triangle. The part of the upper vertex or the base coincides with the median.
- Note that we form two equal right triangles within the equilateral triangle. We trace at height since it always develops 90 with the surface.
- Now, we can use the Theorem. It is enough to replace each piece of information in its place!
Deduce a formula and understand the reasoning used to check it. The history of this formula is as follows: a mathematician knew how to use Pythagoras to calculate the height, but he only used numbers. Thus, it was resolved to substitute the numbers for the letters representing the equilateral triangle parts.
The formula to calculate the height of an equilateral triangle: h = x√3 / 2.
Attention: it helps us add or value height (h) if we turn or side (x). It is enough to substitute the values given, and we will have an answer!
Calculate the height of an equilateral triangle of side 4cm.
It is decked according to the general formula. It is enough to place or 4 instead of x:
- h = x√3 / 2
- h = 4√3 / 2
- h = 2√3
How to calculate the height of any triangle?
OK, here we show you two little points directed to the right triangle. But there is also a method of calculating the heights of random triangles.
To reduce the height of any triangle, or that we do, we use the area formula. We call it “area equal to base times height divided by 2, which can be written as:
A = (b.h)/2
Being that:
- A = area of the triangle.
- b = compression of the triangle base (at the base and where the height is 90).
- h = height of the triangle (a vertex and forms 90 with the base).
You will have the base and the area; substitute a formula to find the height.
And how do I make the area and the base?
It is the measure of any two sides on a very simple basis because every triangle is equal! But, by definition, the base is the side that receives or angle formed when we trace to height.
To find the area, we need the height.
So now to find the height using either Pythagoras or a specific formula yourself!
