Are you confused when understanding difficult concepts of geometry? If so, you are not alone; most students get puzzled when making shapes and finding their height, area, base, hypotenuse, and perpendicular. In this article, we will learn how to find height of a triangle with ease.
What is the Height of a Triangle?
The height of a triangle is the length of a perpendicular straight line originating on a side and intersecting the opposite angle. As we all know, every triangle has three sides, which means every triangle has three heights or altitudes.
However, in an equilateral triangle, each height is the line segment that breaks a side in half and is also an angle split of the opposite angle. That will only occur in an equilateral triangle.
The definition of the Equilateral Triangle is:
“A triangle that has all its sides equal in measurement and each angle measures up to 60 degrees is called an equilateral triangle.”
How to Find Height of a Triangle With Area And Base
If we know the area or base of the triangle, we can use the formula for the area of a triangle to find its height.
The Formula for Area is:
A=1/2bh
A = Area of a triangle
b = length of the base of a triangle
h = Height of the base of a triangle
Look at the triangle and determine which variable value you have. If you know the area, so assign that value to A. You should also see the value of one side length; put that value to “b.”
Remember that any side of a triangle can be the base, regardless of how the triangle is drawn.
For Example
If the area of a triangle is 10, and one side is 8, then:
A = 10 cm
b = 2 cm
Using the area formula for a triangle:
A=1/2 bh
Plugging in the given values:
10 =1/2×8×h
To solve for h, multiply both sides by 2:
20 =8×h
Now, divide both sides by 8:
h=20/8
h=2.5 cm
How to Find Height of an Equilateral Triangle
As we already know, an equilateral triangle has three equal sides, and equal angles that are each 60 degrees. If we cut an equilateral triangle in half, you will get through two congruent triangles. To find the height of an equilateral triangle, we use the Pythagorean Theorem.
Using Pythagorean Theorem
a^2+b^2=c^2
Let’s focus on the lengths of a triangle; angles are useless in the Pythagorean Theorem. The hypotenuse, c, will be equal to the original side length. Side a will be equal to half the side length, and side b will be the height of the triangle we need to solve.
For Example
If we have an equilateral triangle with sides c = 12 and a = 6.
Assign the values to the Pythagorean Theorem and solve for.
a^2+b^2=c^2
〖12〗^2+b^2=6^2
144 = b^2+ 36
b^2=144-36
b^2=108cm
√b = √108
b = 10.392304
So, the height of a triangle is 10.39 or b = 10.39.
That’s how you can find height of an equilateral triangle by using the Pythagorean Theorem. Moreover, you can also find the height of the right angle triangle, isosceles triangle, and equilateral triangle with the Pythagorean Theorem. However, this theorem is not applicable to scalene triangles.
FAQs
What is the Pythagorean Theorem?
The square of the altitude of the hypotenuse of a right-angle triangle equals the sum of the squares of the altitudes of the other two sides, called the Pythagorean Theorem.
What is the formula of the Pythagorean Theorem?
The formula of the Pythagorean Theorem is:
How to find height of a triangle without the area?
If the area of a triangle is not mentioned, but the side altitudes are given, then an easy way to find the height of a triangle is by using the Pythagorean Theorem.
Final Thoughts
Undoubtedly, geometry concepts are hard to understand, and doing their sums is a headache if you don’t know the right formula to apply. But with the right equations you can easily find height, area, and base in a little while. Hope this article on how to find height of a triangle is helpful for you.
