You need to know the height of a triangle to compute its area. Moreover, to determine the height, you must have at least a base. Use these guidelines to determine the height.
- Using Base and Area to Find Height
Remember the formula for the area of a triangle. The formula is A=1/2bh.
Whereas,
A = Area of the triangle
b = Length of the base of the triangle
h = Height of the base of the triangle
- Find The Variables You Are Familiar with By Looking at Your Triangle.
Assign that value to A since you are aware of the area. You should also be aware of the length of one side; give that value to “b”. Regardless of how the triangle is drawn, any side may serve as the base. A simple rotation of the triangle until the given side length is at the bottom will serve as a visual aid.
- Do The Math By Entering Your Values into The Formula A=1/2bh.
Divide the product by the area (A) after multiplying the base (b) by 1/2. This value will determine your triangle’s height!
Finding an Equilateral Triangle’s Height
- Think Back to The Characteristics of An Equilateral Triangle.
Three equal sides and three equal, 60-degree angles make up an equilateral triangle. An equilateral triangle can be divided in half to produce two congruent right triangles.
- Don’t Forget The Pythagorean Theorem.
According to the Pythagorean Theorem, any right triangle with sides measuring a, b, and c, and a hypotenuse measuring a, b, and c, is equal to: a2 + b2 = c2. The height of our equilateral triangle may be determined using this theorem!
- Divide The Equilateral Triangle in Half, and Give The Variables A, B, And C Values.
The length of the original side will be equal to the hypotenuse. Half of the side length will make up side a, and the triangle height we need to solve is determined by side b.
- Calculate b2 By Entering The Values Into The Pythagorean Theorem.
First, multiply each number by itself to square c and a. Afterward, deduct a2 from c2.
- To Determine Your Triangle’s Height, Square The Value Of b2.
Find Sqrt(2 using your calculator’s square root function.
Determining Height with Angles and Sides
- The Variables You are Aware of Should Be Determined.
You may calculate its height if you know a triangle’s two sides, the angle between them, or all three sides. We’ll refer to the triangle’s sides as a, b, and c and its angles as a, b, and c.
- If you have all three sides, you should utilize Heron’s formula and the formula for a triangle’s area.
- Using the formula for the area given two angles and a side, you may get the area if you have two sides and an angle. A = 1/2ab(sin C).
- If You Have Each of The Three Sides, Use Heron’s Formula.
Two elements make up Heron’s formula. The first step is finding the variable s equal to half of the triangle’s perimeter. S = (A+B+C)/2 is used to do this.
- If You Have a Side and An Angle, Use The Formula for The Area Given Two Sides and An Angle.
Substitute the area formula with the area of a triangle formula, which is 1/2bh. You are then presented with a formula that reads 1/2bh = 1/2ab (sin C). Removing one of the side variables this can be condensed to h = a(sin C). Remember that the height you need to determine is across from angle C and side a.
Final Words
Want to know how to find height of a triangle? Then, this article is all for you! Here, we discussed how you could find height of a triangle in different cases. So, have a look!
Also read: Equilateral Triangle: Important Properties, Area and Examples
