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# Law of Sines Calculator

To use the law of sines calculator, select the terms you want to calculate, enter the required values, and hit the calculate button.

Table of Contents:

## Law of Sines Calculator

Law of sines calculator is used to find the unknown value of the sides of a triangle and the angles of the triangle by using the law of Sines of trigonometry.

## What is the Law of Sines?

In trigonometry, the law of sines is used to relate the sides and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides. Mathematically, the law of sines can be expressed as:

**a / sin(A) = b / sin(B) = c / sin(C)**

Where,

**a, b, & c**represent the lengths of the sides of the triangle.**A, B, & C**represent the measures of the angles opposite sides**a, b, & c**respectively.**sin(A), sin(B), & sin(C)**are the sine values of angles**A, B, & C**respectively.

## Examples

Here we solved some examples to understand the working of the Law of Sines Calculator.

**Example 1:**

Evaluate angle “B” if the measurement of angle “A” is 50 degrees, side “a” measured is 8 units, and side b measured 10 units.

**Solution:**

**Step 1:**

Write the data carefully.

Side b = 10, angle A = 50, Side a = 8, angle B =?

**Step 2:**

Write the formula of the Sine Law.

sin(A)/a=Sin(B)/b=Sin(C)/c

**Step 3:**

According to the situation chose the part of the formula and arrange them.

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

Sin(B) = {b × sin(A)}/a

B = Sin^{-1} [{b × sin(A)}/a]

**Step 4:**

Put the values in the above formula and simplify.

B = Sin^{-1} [{10 × sin(50)}/8]

B = Sin^{-1} [{10 × 0.7660}/8]

B = Sin^{-1} [7.660/8]

B = Sin^{-1} [0.9576]

**B = 73.25 ^{0}**

**Example 2:**

Evaluate angle “A” while the measurement of angle “B” is 50 degrees, side “a” measured is 10 units, and side b measured 8 units.

**Solution:**

**Step 1:**

Write the data carefully.

Side b = 8, angle B = 50, Side a = 10, angle A =?

**Step 2:**

Write the formula of the Sine Law.

sin(A)/a=Sin(B)/b=Sin(C)/c

**Step 3:**

According to the situation chose the part of the formula and arrange them.

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

Sin(A) = {a × sin(B)}/b

A = Sin^{-1} [{a × sin(B)}/b]

**Step 4:**

Put the values in the above formula and simplify.

A = Sin^{-1} [{10 × sin(50)}/8]

A = Sin^{-1} [{10 × 0.7660}/8]

A = Sin^{-1} [7.660/8]

A = Sin^{-1} [0.9576]

**A = 73.25 ^{0}**