# Solving Formulas For Triangles

Introduction

A triangle has three sides. Three intersecting lines are used to form the triangle. The total angle of the triangle is 180 degree. Triangle has three angles and three vertices. Triangles are classified based on sides and angles. There are different formulas are used for solving the triangles. In solving triangle, pythagoras theorem is used for finding the sides of the triangle. Based on sides triangles are classified as, isosceles triangle, equilateral triangle, and scalene triangle. Based on angles triangles are classified as, right angle triangle, obtuse triangle, acute triangle.

## Solving formulas for triangles - formulas

Formula for right angle triangle:

Area of the right triangle is = (1 / 2) * b * h

Here, b = base and h = height

Formula for finding side length:

Using pythagoras theorem

A2 = B2 + C2

Here, A = hypotenuse, B = opposite side, C = adjacent side

Formula for equilateral triangle:

Area of the equilateral triangle = √3 * (s / 2)2

Here, s = side length.

Using heron's formula:

Area of the triangle = `sqrt(s (s - a) (s - b) (s - c))`

Here, s = (a + b + c) / 2, a, b, c are side length.

## Example problem for solving triangles

Solving formulas for triangles    example 1:

Solve and find the area of the triangle with the base is 45 cm and height is 22 cm.

Solution:

Given base = 45 cm, height = 22 cm

Formula:

Area of the triangle = (1 / 2) * b * h

Substitute the given value in the above equation, we get

= (1 / 2) * 45 cm * 22 cm

=  495 cm2

The final answer is 495 cm2

Solving formulas for triangles    example 2:

Solve the given triangle problem. Two sides of the triangles are 15 cm and 20 cm. Find the third side of the triangle.

Solution:

Given two sides are B = 15 cm, C = 20 cm

Formula:

Using pythagoras theorem,

A2 = B2 + C2

= 152 cm + 202 cm

= 625 cm

Take square root on both sides, we get

A = 25 cm

The final answer is 25 cm

Solving formulas for triangles    example 3:

Solve for finding area of the equilateral triangle with side length is 12 cm.

Solution:

Given side length s = 12 cm

Formula:

Area = √3 * (s / 2)2

= √3 * (12 / 2)2

= 10.39 cm2