# Law of Sines Calculator

Law of Sines Calculator computes the value of the unknown side when one side is known and the angles subtended by the known and unknown sides are given. The sine rule is an equation that gives the relationship between the sides and angles of a non-right triangle.

## What is the Law of Sines Calculator?

Law of Sines Calculator is an online tool that helps to calculate the length of the unknown side of a triangle when we know the measure of one side as well as the angles subtended by both the known and the unknown sides. To use the * law of sines calculator*, enter the values in the given input boxes.

### Law of Sines Calculator

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

## How to Use Law of Sines Calculator?

Please follow the steps below to find the value of the unknown side of a triangle using the law of sines calculator.

**Step 1:**Go to Cuemath's online law of sines calculator.**Step 2:**Choose the known side from the drop-down list (a or b). Enter the values in the input boxes.**Step 3:**Click on the**"Calculate"**button to find the length of the unknown side.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Law of Sines Calculator Work?

The law of sines helps to give a relationship between the side lengths of a triangle and the sine of their opposite angles. Let a, b, and c be the length of the three sides of a triangle. Further let A, B, and C be the angles opposite to the sides a, b, and c respectively. The formula for the sine law is given as follows:

a / sinA = b / sinB = c / sinC

We can also represent this formula in two other different ways. These are as follows:

sinA / a = sinB / b = sinC / c

a / b = sinA / sinB; a / c = sinA / sinC; b / c = sinB / sinC

The steps to calculate the value of the unknown side (either a or b) are as follows:

- Suppose we know the value of a, A, and B. Then the formula to calculate the length of b is given as b = a × sinB / sinA.
- Suppose we know the value of b, A, and B. Then the formula to calculate the length of a is given as a = b × sinA / sinB.

## Solved Examples on Law of Sines

**Example 1: **Given a triangle ABC, if a = 5 units, A = 60 degrees, and B = 30 degrees, then find the length of b. Verify it using the online law of sines calculator.

**Solution:**

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

a / sinA = b / sinB

b = a × sinB / sinA

b = 5 × (sin(30) / sin(60) )

b = 2.886 units

**Example 2: **Given a triangle ABC, if b = 12.5 units, A = 30 degrees, and B = 15 degrees, then find the length of a. Verify it using the online law of sines calculator.

**Solution:**

Given Length of the side b = 12.5 units, A = 30 degrees, B = 15 degrees

a / sinA = b / sinB

a = b × sinA / sinB

a = 12.5 × (sin(30) / sin(15) )

a = 6.4705 units

Similarly, you can try the law of sines calculator to find the length of the unknown sides for the following:

- Length of the b side = 5 units, A = 60 degrees, B = 15 degrees
- Length of the a side = 10.5 units, A = 12 degrees, B = 43 degrees

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