# Sinus theorem calculator

## Theorems

## Sinus theorem

Our sinus theorem calculator makes it easy for you to find the missing side or angle of a triangle using the sinus theorem. Simply enter the known values into the calculator, and it will automatically calculate the missing value for you. This tool is perfect for students, teachers, and anyone else who needs to solve triangles quickly and accurately.

## What is the Sinus Theorem?

The sinus theorem, also known as the law of sines, is a trigonometric formula used to solve triangles. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words, the ratio of the length of a side to the sine of its opposite angle is a constant value.

## Sinus Theorem Formula

The formula for the sinus theorem is:

\dfrac{a}{sin(\alpha)} = \dfrac{b}{sin(\beta)} = \dfrac{c}{sin(\gamma)} = 2R

Where a, b, and c are the lengths of the sides of the triangle, and α, β, and γ are the angles opposite those sides, and R is the radius of circumscribed circle.

### Example

Find the length of side b in a triangle with sides a = 5, c = 7, and angle α = 30 degrees.

Using the sinus theorem formula:

\dfrac{a}{sin(\alpha)} = \dfrac{b}{sin(\beta)} = \dfrac{c}{sin(\gamma)} = 2R

\dfrac{5}{sin(30^0)} = \dfrac{b}{sin(\beta)} = \dfrac{7}{sin(\gamma)} = 2R

sin(\gamma) = \dfrac{7*sin(30)}{5} = 0.7 \implies \gamma = 44.4^0

\beta = 180 - 30 - 44.4 = 105.6^0

b = \dfrac{sin(105.6^0)*5}{sin(30^0)}

b = \dfrac{5*0.96}{0.5} = 9.6

Therefore, the length of side b is approximately 9.6 cm.

## Conclusion

In conclusion, the sinus theorem is an important formula used to solve triangles. Our sinus theorem calculator makes it easy for you to solve triangles quickly and accurately. Whether you are a student, teacher, or anyone else who needs to solve triangles, our calculator will help you get the job done. So, use our calculator today and make your calculations easier!

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