Sides of Triangle Formula

Sides of Triangle Formula

Each side of a triangle is represented by a straight line. These lines meet each other to form three vertices. Pythagoras theorem is applied to determine the sides of any right-angled triangle.

When some side lengths and other angles are provided, we apply the cosine law or the sine law to get the length of any side of a given triangle.

After reading this article, you will get to know about the sides of the triangle formula along with a few properties of the sides. We have also solved a couple of examples to clear your doubt.

What are Sides of Triangle Formula?

For a right-angled triangle, refer to the Pythagorean Theorem without any hesitation.

To find the lengths of sides of any isosceles triangle, we may use the perimeter or area formula.

For a general triangle, where some angles and some sides are given, we utilize the sine law or the cosine law.

1. If we know a side and an angle of a right-angled triangle,

Sin θ = opposite side’s length/hypotenuse

Cos θ = adjacent side’s length/hypotenuse

Tan θ = opposite side’s length/adjacent side’s length

2. Law of sines is given as: sin(A)/a = sin(B)/ b = sin(C)/c

Here, the three sides are represented by a, b and c while the corresponding angles are taken as A, B and C respectively.

3. Law of cosines is given as: c² = b² + a² – 2ab. Cos (C)

Here, C represents the angle created by a and b sides. The three sides of this triangle are a, b and c.

Properties of a triangle’s sides

• Perimeter of a triangle = sum of its sides

• Any two triangles are identical when their corresponding sides appear to be proportional

• The side which remains opposite to the maximum angle of any triangle is its longest side

Solved Examples

1. Triangle XYZ’s perimeter is 160 cm. Length of side XY is 60cm while that of YZ is 50 cm. Determine the length of ZX. 

Solution: From the perimeter formula it can be written: XY + YZ + ZX = perimeter

Putting the values we see: 60 + 50 + ZX = 160

Therefore, ZX = 160 – (60 + 50) = 50 cm.

Answer: Length of ZX is 50 cm.

2. In a right triangle the hypotenuse is 16 cm. A random side is 8 cm. Find the third side applying the Pythagoras theorem.

Solution: The Pythagorean formula is written as:

Hypotenuse² = height² + base²

Or, 16² = 8² + base²

Or, base² = 256 – 64 = 192

Determining the square root we get the base as 13.85 cm.

Answer: 13.85 cm.

Important formulas: