Solve for X in Degrees Calculator

This calculator helps you find the unknown angle (x) in a triangle when you know two sides and one angle, or two angles and one side. It uses the Law of Sines or Law of Cosines depending on the given information.

How to Use This Calculator

To solve for x in degrees:

Select whether you're solving using the Law of Sines or Law of Cosines.
Enter the known values in the appropriate fields.
Click "Calculate" to find the unknown angle.
Review the result and any additional information provided.

The calculator will automatically determine which formula to use based on the information you provide.

Formula Used

The calculator uses two main formulas depending on the given information:

Law of Sines: (a / sin A) = (b / sin B) = (c / sin C) For angle x: sin x = (side opposite x / side opposite known angle) × sin(known angle)

Law of Cosines: c² = a² + b² - 2ab cos C For angle x: cos x = [(a² + b² - c²) / (2ab)]

Where:

a, b, c are the lengths of the sides of the triangle
A, B, C are the angles opposite sides a, b, c respectively
x is the unknown angle we're solving for

Worked Examples

Example 1: Using the Law of Sines

Given a triangle with sides a=5, b=7, and angle A=30°, find angle B.

Using the Law of Sines:

sin B = (b / a) × sin A sin B = (7 / 5) × sin(30°) sin B = 1.4 × 0.5 sin B = 0.7 B ≈ 44.42°

Example 2: Using the Law of Cosines

Given a triangle with sides a=4, b=6, and c=5, find angle C.

Using the Law of Cosines:

cos C = [(a² + b² - c²) / (2ab)] cos C = [(16 + 36 - 25) / (48)] cos C = 27 / 48 cos C = 0.5625 C ≈ 55.77°

Frequently Asked Questions

When should I use the Law of Sines vs. the Law of Cosines?

Use the Law of Sines when you know two angles and one side, or two sides and one angle (not the included angle). Use the Law of Cosines when you know all three sides, or two sides and the included angle.

What if I get multiple solutions for angle x?

In some cases, especially when using the Law of Sines, you might get two possible solutions (one acute and one obtuse) for angle x. You'll need additional information to determine which solution is correct for your specific triangle.

What if the calculation results in an angle greater than 180°?

If the calculation results in an angle greater than 180°, it means the triangle is not possible with the given side lengths and angles. Double-check your input values.