# Recommended area calculators for students to solve trigonometric equations

Using trigonometry can solve many problems precisely where you might only be able to approximate before. Trigonometry is widely used in everything from engineering and architecture to GPS, business, surveying, navigation, astronomy and the physical sciences. Before going to the solution of trigonometric equations, you might want to know more about trigonometric equations and trigonometric functions.

#### What are trigonometry and trigonometric equations?

The word TRIGONOMETRY (combination of Greek words), TRI which means THREE, GON which means CTÉS and METRON which means measure. Thus, trigonometry is an important branch of mathematics that studies triangles and the relationship between their sides and the angles between their sides. Simply put, it means the measurement of the triangle.

The equations that involve the **trigonometric functions** are called trigonometric equations. Solving a trigonometric equation and an algebraic equation, such as finding the value of the variable that satisfy the equation, is almost similar. The trigonometric functions are mainly three *sin, cos and tan *etc.

#### Trigonometric functions:

The six trigonometric functions for any acute angle of a right triangle *ABC* as the figure shows as you know, trigonometry deals with right angles. The right triangle is one that makes an angle of 90. The side opposite the right angle is called the hypotenuse. The other two sides are adjacent and opposite.

#### What is the solution of a triangle?

As we have seen, a triangle has six important factors; three angles and three sides. If any one of three of these six elements, including at least one side, is given, the remaining three elements can be determined. These unknown items can be discovered by a method called **solution of a triangle**. Thus, in solving triangles, we may encounter some problems regarding the angle of measurements, heights and distances, angle of elevation and depression, oblique triangles and area of triangles, etc. And here our main concern is to find the **area of the triangle using calculators.**

#### Triangular area formula

The area of a triangle is the total space covered by the three sides of the triangle. In simple math questions, we use the following formula to find the area.

Where b represents the base and h represents the height of the triangle. But, in trigonometry, the rule for finding the area is slightly different because trigonometry concerns the measurement of angles.

For example

If you have a triangle with a base measuring 4 cm long, and a height measuring 8 cm long. We will put these given values into the formula to get the answer.

#### Formula for the area of a triangle.

As you already know the formula:

Here, b is the length of the base of the triangle and h is the height of the triangle.

#### By putting base lengths and height in the formula.

Multiply the two values together, then divide their product by 2. You will get the area of the triangle in square units.

There are a number of equations for calculating the area of triangles in trigonometry, all based on the required information in question. Three of them, are given below

- Area of the triangle in terms of the measurement of two sides and their included angles.
- Area of a triangle in terms of the measure of one side and two angles.
- Area of the triangle in terms of the measurements of its sides, also known as the hero’s formula.

On top of these three methods for finding the area of a triangle, the third solving using the hero’s formula as well as a simple triangle area formula can be calculated using online calculators.

#### The hero’s formula:

Hero’s formula is used to find the area of the triangle when the lengths of all sides are known. The formula is attributed to Hero of Alexandria, Greek engineer and mathematician. Basically it is used to find the area of any triangle based on the lengths of the three sides *a*, *b*, and *vs.*

Right here, *a, b and c *are the lengths of the triangle and s is a half perimeter which is equal to half the sum of the three sides.

First, you need to find the value of the semi-perimeter, then put the values of the three lengths of the triangle into the formula to get the answer.

#### Online calculators for the area of the triangle:

The area of a triangle calculator helps students find the area of a triangle with one click.

There are a number of websites online that provide free tools for calculating the area of triangles in trigonometry. Either we calculate the area of the triangle using a simple formula or the hero formula, these calculators provide their services to get the solution in a quick way. We use different equations to find the area in trigonometry and it largely depends on the information given to us.

Some of the recommended online calculator websites that provide free tools for students to find area calculations are given here;

All of these websites have a triangular area calculator which will allow you to learn and compose trigonometric operations without any hassle. Simply, they can help find the area of the triangle in both directions, in a simple way and by the hero formula. Moreover, these websites are the cheapest means of computing and they are very easy to use.

#### How to use the area calculator:

These online tools feature two calculators for calculating the triangular area, either by a simple triangular area formula or by the hero formula.

#### Triangular area calculator

Suppose you know the two sides of a triangle, the height and the base and the angle between them. All you gotta do is

Enter length or height

It is for example equal to 8cm.

Put the second side or base of the triangle

Suppose it is 5cm tall.

Determine the angle between these two sides

For example, 30 degrees.

· The triangular area calculator will display the answer after all calculations.

The area of the triangle would be equal to 20 cm^{2}.

The same is how you can use the hero’s formula calculator to calculate the area of the triangle.

#### Conclusion:

So, these area calculator online tools not only save a lot of time because you don’t have to write a formula to get the answer, but they are also much easier to use. Besides, they save money so that everyone can enjoy them just by clicking on the keyboard. And these calculators are not just tools for use by students, but engineers, astronomers, physicists and social scientists and just about anyone involved in trigonometry.

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