# Law of Sines Calculator

Sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.

## What is the Law of Sines Calculator?

'Cuemath's Law of Sines Calculator' is an online tool that helps to calculate the length of the side of a triangle. Cuemath's Comparing Law of Sines Calculator helps you to calculate the length of the side of a triangle within a few seconds.

NOTE: Please enter the values up to 5 digits only.

## How to Use Law of Sines Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter the length of the side (x), the angle subtended by known side (a) and unknown side(b) in the given input box.**Step 2:**Click on the**"Calculate"**button to find the length of the unknown side.**Step 3:**Click on the**"Reset"**button to clear the fields and enter new values.

## How to Find the Side of a Triangle?

A Law of sines is a law of trigonometry that states that the proportion between the length of a side of a triangle to the sine of the opposite angle is equal for each side.

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

Where a, b, c are the side lengths of the triangle and A, B, C are angles opposite to them respectively.

**Solved Example:**

Find the length of unknown side 'b' for triangle where length of side 'a' is 5 units, angle subtended by side 'a' is 60 degrees and angle subtended by unknown side 'b' is 30 degrees.

**Solution:**

Given Length of the side a = 5 units, A = 60°, B = 30°

a/sin(A) = b/sin(B)

b = a sin(B) / sin(A)

b = (5*sin(30)°) / sin(60)°

b = 2.886 units

Similarly, you can try the calculator to find the length of side for the following:

- Length of the b side = 5 units , A = 60°, B = 60°
- Length of the a side = 10 units , A = 37°, B = 53°