In geometry, to find the sides of a triangle, we have many methods such as Pythagoras theorem, Sine and Cosine rule or by angle sum property of triangle. These methods are applicable based on the conditions or the parameters given to us.
Also, we will come across different types of triangles based on the length of the sides. Basically, there are three types, based on sides of the triangle, which are:
- Scalene Triangle
- Isosceles Triangle
- Equilateral Triangle
Scalene Triangle: The triangle where all sides are unequal.
Isosceles Triangle: The triangle where only two sides are equal, and the angles opposite the equal sides are also equal.
Equilateral Triangle: The triangle where all three sides are equal, and also all the angles are equal to 60 degrees.
Finding Sides of a Triangle
We can find not only the sides of the triangle but also the angles of the triangle using the methods mentioned in the introduction. Below is a brief of Pythagoras theorem.
Pythagoras theorem: In a right triangle, if hypotenuse, perpendicular and base are its sides, then as per the theorem, the square of hypotenuse side is equal to the sum of the square of base and square of perpendicular.
Hypotenuse2 = Base2 + Perpendicular2
Hence, if we know any two sides, then we can easily find the third side of the triangle.
Similarly, as per angle sum property, the sum of all the interior angles of a triangle is always equal to 180 degrees.
How to find the length of a triangle given one side and angle?
If we are given an angle and a side length, then we can use trigonometry ratios to find the other two sides. As per the sine, cosine and tangent ratios, in a triangle, if θ is the angle between two sides, then;
Sine θ = Length of opposite side/Length of Hypotenuse side
Cos θ = Length of Base side/Length of Hypotenuse side
Tan θ = Length of Perpendicular side/Length of Base side
Using Perimeter Formula
The perimeter of any triangle is equal to the sum of all its sides. It is the total length of any triangle. Suppose a triangle ABC is given, then as per the formula;
Perimeter of ABC = AB + BC + AC
If we know the length of any two sides and perimeter of the triangle, then we can easily find the length of the third side.
Example: The perimeter of a triangle ABC is 150 cms and the length of the two sides AB and BC is 50cm and 60 cms, respectively. Then, find the length of the third side.
Solution: Given, perimeter = 150 cms
AB = 50cm
BC = 60cm
As per the perimeter formula, we know;
Perimeter = AB + BC + AC
Putting the values;
150 = 50+60+AC
AC = 150 – 110
AC = 40 cm
Hence, the length of the third side is 40 cm.