Trigonometry in Calculator
Trigonometry can be a challenging subject, but with the right tools, it becomes much more manageable. Our trigonometry calculator is designed to help …
Go to calculator →The cosine law, also known as the law of cosines, is a fundamental trigonometric principle used to solve triangles. Whether you’re a student tackling geometry homework or an engineer working on complex designs, our Cosine Law Calculator simplifies the process of finding unknown sides and angles in triangles.
The cosine law relates the lengths of the sides of a triangle to the cosine of one of its angles. It’s particularly useful when dealing with non-right triangles where the Pythagorean theorem doesn’t apply.
The formula for the cosine law is:
c² = a² + b² - 2ab cos(C)
Where:
Choose the type of triangle problem you’re solving:
Enter the known values:
Click “Calculate” to get your results instantly
The calculator will display the unknown angles or side length, depending on your input
Given:
To find angle C:
cos(C) = (a² + b² - c²) / (2ab) cos(C) = (5² + 7² - 8²) / (2 _ 5 _ 7) C ≈ 82.82°
Given:
To find side c:
c² = a² + b² - 2ab cos(C) c² = 10² + 12² - 2 _ 10 _ 12 * cos(60°) c ≈ 10.39 m
The cosine law has numerous real-world applications:
Ready to solve your triangle problems? Try our Cosine Law Calculator now and experience the ease of trigonometry calculations at your fingertips!
Use the cosine law when you have either all three sides (SSS) or two sides and the included angle (SAS) of a triangle. The sine law is better for AAS (Angle-Angle-Side) or ASA (Angle-Side-Angle) triangles.
Yes, the cosine law works for all triangles, including right triangles. However, for right triangles, the Pythagorean theorem is often simpler to use.
Our calculator uses precise mathematical algorithms and provides results accurate to several decimal places, suitable for most practical applications.
The cosine law is primarily for 2D triangles. For 3D problems, you might need to break down the geometry into 2D components or use more advanced tools.
While it's possible to solve triangles manually using logarithm tables or approximation methods, a calculator greatly simplifies the process and improves accuracy.
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