Finding The Height of An Equilateral Triangle

An equilateral triangle is a three-sided polygon with three equal sides and three equal angles. Finding the height of an equilateral triangle is a common problem in geometry and trigonometry. In this article, we will walk through the steps necessary to find the height of an equilateral triangle having side 2a.

Understanding the Basics

Before we dive into the calculations, it is important to understand the basics of an equilateral triangle. An equilateral triangle has three equal sides, all of which have the same length. This means that all the angles in an equilateral triangle are also equal. The angles of an equilateral triangle are all 60°. Knowing this information is important when trying to calculate the height of an equilateral triangle.

Using the Pythagorean Theorem

The Pythagorean theorem can be used to find the height of an equilateral triangle. The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse. To find the height of an equilateral triangle, we must first find the length of the hypotenuse.

Finding the Hypotenuse

To find the hypotenuse of an equilateral triangle, we can use the formula for the side of an equilateral triangle. The formula for the side of an equilateral triangle is given by 2a. We can then use this formula to find the length of the hypotenuse, which is equal to 2a√3. Now that we have the hypotenuse, we can use the Pythagorean theorem to find the height of the triangle.

Using The Pythagorean Theorem to Find The Height

Using the Pythagorean theorem, we can find the height of an equilateral triangle. The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse. In this case, the two shorter sides are equal to 2a and the hypotenuse is equal to 2a√3. Thus, the height of the triangle is equal to 2a√3-2a. This means that the height of an equilateral triangle having side 2a is equal to 2a√3-2a.

Finding The Area of The Triangle

The area of an equilateral triangle can be found using the formula for the area of a triangle. The formula for the area of a triangle is given by A=1/2bh, where b is the base of the triangle and h is the height of the triangle. In this case, the base of the triangle is equal to 2a and the height is equal to 2a√3-2a. Thus, the area of an equilateral triangle having side 2a is equal to 1/2(2a)(2a√3-2a), which is equal to 4a²√3-4a².

Conclusion

In conclusion, finding the height of an equilateral triangle having side 2a can be done using the Pythagorean theorem. The hypotenuse of the triangle is equal to 2a√3 and the height of the triangle is equal to 2a√3-2a. Using these values, the area of the triangle can also be found. Knowing the height of an equilateral triangle is an important skill for anyone studying geometry or trigonometry.