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Law of Sines Calculator
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Law of sine calculator or Sine Calculator applies the laws of sine to find the unknown sides and angles of any triangles. For calculating the known sides and angles you should enter the three known values in the below calculator.

You can see a default angles and sides given below and Click on "Calculate". In this case, we need to find side "b", b is calculated by using sine law.
 

Steps for finding unknown values using Laws of Sines

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Step 1 :  

For calculating any angles, For example, if you like to calculate the angle 'B', enter its known value 'b'. Follow the same step for both 'A' and 'C'.



Step 2 :  

The calculator follows SSA (Side side angle) and uses sine laws for calculating the unknown values.



Example Problems on Laws of Sines

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  1. Find the value of c when B = 30°, C = 110° and b = 8.


    Step 1 :  

    Sine law: $\frac{a}{sin A}$= $\frac{b}{sin B}$ = $\frac{c}{sin C}$
    $\frac{a}{sin A}$ = $\frac{8}{sin(30°)}$ = $\frac{c}{sin(110°)}$
    As $\frac{a}{sin A}$ is not useful in this case let us ignore it. So we get $\frac{8}{sin(30°)}$ = $\frac{c}{sin(110°)}$



    Step 2 :  

    Let's interchange the sides, so we get $\frac{c}{sin(110°)}$ = $\frac{8}{sin(30°)}$
    Multiplying both side by sin(110°), c = ($\frac{8}{sin(30°))}$ x sin(110°)
    c = ( $\frac{8}{0.5}$ × 0.939...



    Answer  :  

    Therefore, c = 15.024



  2. Find angle 'B'. Where, C = 75°, b = 4.2, c = 5.7.


    Step 1 :  

    Sin law: $\frac{Sin A}{a}$ = $\frac{Sin B}{b}$ = $\frac{Sin C}{c}$
    $\frac{Sin A}{a}$ = $\frac{Sin B}{4.2}$ = $\frac{Sin(75º)}{5.7}$
    As $\frac{in A}{a}$ is not useful in this case let us ignore it. So we get $\frac{Sin B}{4.2}$ = $\frac{Sin(75º)}{5.7}$



    Step 2 :  

    Multiplying both side by 4.2, Sin B = $\frac{sin75º}{5.7}$ × 4.2
    Hence, Sin B = 0.7117...
    Sine Inverse: B =  sin-1(0.7117...)



    Answer  :  

    B = 45.3º



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