Law of Sines Calculator
Use the law of sines to solve a triangle. Give a known angle and the side opposite it, add one more angle or side, and get the remaining angles and sides.
How to use the law of sines
- Enter the known angle A and the side a opposite it.
- Add either angle B (to find side b) or side b (to find angle B).
- Read angle C and the remaining sides, computed from the common ratio.
Examples
Angle B given
angle A = 30, side a = 10, angle B = 45
side b 14.1421, angle C 105, side c 19.3185
Side b given (acute solution)
angle A = 30, side a = 10, side b = 14.1421
angle B 45, angle C 105, side c 19.3185
Frequently asked questions
What is the law of sines?
The law of sines says each side divided by the sine of its opposite angle gives the same ratio. That common ratio links every side and angle in the triangle.
What inputs does this calculator need?
It needs a known angle and the side opposite it, plus one more value: either a second angle to find its opposite side, or a second side to find its opposite angle.
Why does it return the acute angle when I give a side?
Finding an angle from a side uses the inverse sine, which can have two answers (the ambiguous case). This tool reports the acute solution, which is the most common.
When is there no solution?
If the given side opposite the unknown angle is too long, the sine ratio exceeds one and no triangle exists, so the calculator reports an error.
Are angles in degrees or radians?
Angles are entered and reported in degrees. They are converted to radians internally before the sine is taken, using radians equal to degrees times pi over 180.
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