Law of Sines Calculator

This Law of Sines Calculator helps you find missing side lengths in a triangle when two angles and one opposite side are known. It uses the formula a / sin(A) = b / sin(B) = c / sin(C) to relate side lengths to their opposite angles. First find the third angle, then use the law of sines to calculate the missing sides. It is a simple way to check answers, understand the law of sines, and practise basic trigonometry step by step.

Step-by-step method

1. Identify what is given.
2. Find the third angle.
3. Use the Law of Sines to find the missing sides.
4. Write the final answers.

Formula:

Example 1: A = 40°, B = 60°, a = 10

Step 1 - Identify what is given.

In this problem: The given values are A = 40°, B = 60°, and a = 10.

Step 2 - Find the third angle.

In this problem: Angles in a triangle add to 180°, so C = 180° − A − B = 80°.

Step 3 - Use the Law of Sines to find the missing sides.

In this problem: Use the Law of Sines for b: b = a · sin(B) / sin(A).

Step 4 - Use the Law of Sines to find the missing sides.

In this problem: Use the Law of Sines for c: c = a · sin(C) / sin(A).

Final answer: b = 13.47296355, c = 15.32088886

Example 2: A = 30°, B = 70°, a = 12

Step 1 - Identify what is given.

In this problem: The given values are A = 30°, B = 70°, and a = 12.

Step 2 - Find the third angle.

In this problem: Angles in a triangle add to 180°, so C = 180° − A − B = 80°.

Step 3 - Use the Law of Sines to find the missing sides.

In this problem: Use the Law of Sines for b: b = a · sin(B) / sin(A).

Step 4 - Use the Law of Sines to find the missing sides.

In this problem: Use the Law of Sines for c: c = a · sin(C) / sin(A).

Final answer: b = 22.5526229, c = 23.63538607