## Introduction to the Law of Sines Calculator:

Law of sines calculator is an online tool that helps you to find the triangle using the law of sine equation in a few seconds. It is used to simplify the process of **solving triangles** and make it easier to find unknown sides and angles.

Law of sine calculator is very beneficial for students, teachers, and researchers who do not want to evaluate the angle of a triangle by hand. This tool give the solution of sine rule problem using the law of sine easily.

## What is the Law of Sines?

The Law of Sines is defined as the length of a **side of a triangle** over the sine of its opposite angle for all three sides (a,b,c) and angles (A, B, C) of the triangle. It is a fundamental principle In trigonometric function that applies to any triangle.

It is a useful concept for many fields like working with geometric and trigonometric problems in mathematics, and engineering to find the length and side of a particular object.

## Formula of Law of Sine:

The **laws of sine formula** are used to find the unknown side lengths or angles of a triangle. The sides of a triangle are indicated by a,b, and c, whereas the angle opposite side is A, B, and C.

You can solve any sine-related queries by using the law of sines calculator but If you are trying to solve sine equations manually the below formula will be very helpful for you.

$$ \frac{a}{sin(A)} \;=\; \frac{b}{sin(B)} \;=\; \frac{c}{sin(C)} $$

## How to Calculate the Law of Sines?

To **calculate the value** of a given triangle using the law of sine equation, this process involves solving the unknown angles or sides in a triangle when you have at least some of the angles and sides.

The law of sines solver uses orderly steps to simplify a given sine expression. Follow these step-by-step instructions:

**Step 1**:

Identify the given angle value and length of the side of the triangle.

**Step 2**:

If you have two angle values then first find the value of the third angle using the below formula.

$$ C \;=\; 180∘ − A − B $$

**Step 3**:

Use the formula of the law of sine to find the length of sides of triangles a,b, and c.

$$ \frac{a}{sin\; A} \;=\; \frac{b}{sin\; B} \;=\; \frac{c}{sin\; C} $$

**Step 4**:

Rearrange the formula of the law of sine as you find the value of a,b, and c of the given triangle.

$$ \frac{a}{b} \;=\; \frac{sin\; A}{sin\; B},\; \frac{a}{c} \;=\; \frac{sin\; A}{sin\; C},\; \frac{b}{c} \;=\; \frac{sin\; B}{sin\; C} $$

**Step 5**:

Add the value in the law of the sine formula and simplify it to get the length of the a,b, and c of the given triangle. You can get the answer directly by using the law of sines calculator triangle.

## Solved example of the law of sine:

A solved **example** of the law of sine gives you a better understanding of the law of sine calculation procedure. Basically it is necessary to follow the rule of sines that is used to solve sine examples.

**Example**:

Solve the triangle Δ ABC given a = 10, A = 41°, and C = 75°.

**Solution**:

Identify the given data a = 10 ,A = 41, C = 75

First, find the missing angle value B = ?

$$ C \;=\; 180° − A − B $$

Rearrange the equation to find the value of B

$$ B \;=\; 180° − 41 − 75 $$

$$ B \;=\; 64° $$

Using the law of sine to find the sides of a given triangle b and c.

$$ \frac{a}{sin\; A} \;=\; \frac{b}{sin\; B} \;=\; \frac{c}{sin\; C} $$

### PASTE THE GRAPH HERE!

Rearrange the above law of sine formula to find the length of b and c.

$$ \frac{a}{b} \;=\; \frac{sin\; A}{sin\; B},\; \frac{a}{c} \;=\; \frac{sin\; A}{sin\; C},\; \frac{b}{c} \;=\; \frac{sin\; B}{sin\; C} $$

For the value of b the law of sine formula is:

$$ \frac{b}{sin\; B} \;=\; \frac{a}{sin\; A} ⇨ b \;=\; \frac{a\; sin\; B}{sin\; A} $$

Put the value to find the value of b,

$$ =\; \frac{10\; sin\; 64°}{sin\; 41°} ⇨ b \;=\; 13.7 $$

For the value of c the law of the sine formula is,

$$ \frac{c}{sin\; C} \;=\; \frac{a}{sin\; A} ⇨ c \;=\; \frac{a\; sin\; C}{sin\; A} $$

Put the value in the above formula to get the value of c.

$$ =\; \frac{10\; sin\; 75°}{sin\; 41°} ⇨ c \;=\; 14.7 $$

As you know how to solve these problems manually so let us understand how to use the law of sines calculator easily.

## How to Use Law of Sine Calculator?

The sine law calculator has a simple design that makes it easy for you to know how to use it for the evaluation of complex law of sine function problems in some simple steps.

- Enter the value of the angle of the given triangle in the given input field.
- Enter the value of the side of the triangle in the input field of law of sin calculator.
- Recheck the given complex triangle values before clicking on the calculate button to start the evaluation process in the sine rule calculator.
- Click the “
**Calculate**” button to get the result of your given complex law of sine problem. - If you are trying our calculator for the first time then you can use the load example to learn more about this concept.
- Click on the “Recalculate” button to get a new page for finding more example solutions to complex law of sine problems.

## Result from Law of Sines Solver:

Law of sin calculator gives you the **solution** from a given complex law of sine function when you add the input into it. It included as:

**Result Option**:

When you click on the result option the law of sine calculator gives you a solution to the given law of sine function.

**Possible Steps**:

When you click on it, this option will provide you with a solution where all the calculations of the law of sine are mentioned.

## Benefits of Using the Sine Rule Calculator:

The sine law calculator provides you with tons of **benefits** that help you to calculate complex laws of sine problems and give you solutions without any trouble. These benefits are:

- It is a free-of-cost tool so you can use it for free to find complex laws of sine problem solutions without spending.
- Law of sines triangle calculator is a manageable tool that can manage various types of trigonometric sine function problems because it has advanced features in its server.
- It gives you conceptual clarity for the law of the sine function process when you use it for practice to solve more examples.
- Laws of sines calculator save the time that you consume on the calculation of complex law of sine function problems manually.
- It is a reliable tool that provides you with accurate solutions whenever you use it to calculate complex law of sine problems without any man-made mistakes.
- Sine rule calculator allows you to use it multiple times for the evaluation of complex law of sine problems.