What is a Triangle?
In order to calculate height of a triangle, we need to know what a triangle is. A triangle is one of the basic shapes in geometry. It is a polygon formed by three line segments linked end-to-end also known as edges and three vertex.
There several different types of triangles but all of them have three sides.
Types of Triangles.
- Equilateral triangle. This type of triangle is also known as an equiangular triangle it has three equal line segments or three equal sides.
- Isosceles triangle. This is a type of triangle whose at least two sides or edges are equal.
- Right-angled triangle. This is a type of triangle that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
Formula to Calculate the Height of a Triangle.
To calculate the height of a triangle, it is important to identify the type of the three-sided polygon in question. Is it an equilateral triangle, an isosceles triangle or a right angle triangle as each of these triangle require specific formulas when calculating their height.
How to Find the Height of a Right Angle Triangle.
The most basic formula to calculate the area of a triangle is;
From the above formula we get;
Example 1:
Calculate the height of a right-angled triangle whose area is25 cm² and the given length of its base is 10 cm.
Therefore the height of the triangle is 5 cm.
How to Find an Isosceles Triangle’s Height.
To find the height of this type of triangle, we use the Pythagorean theorem. Whereby, the length of the hypotenuse squared is equal to the sum of the length of the base squared and the height squared, as in;
Therefore, to get the height, we have to use our knowledge on algebra and by making the height or in our case c the subject c, we get;
Example 2:
Calculate the height of an isosceles triangle if the length of its hypotenuse is 5cm and the base is 3cm, calculate the height.
16 is height squared. Therefore, to find the height or a, we find the square root of 16 which is 4. Hence, the height of the triangle is 4cm.
There are more methods to calculate the height of a triangle and they are;
- Using angles and sides.
- Using the Heron’s formula.
Finding the height of a triangle is a multi-step process that can be confusing but once you identify what you are dealing, it becomes easier.
