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Law of Cosines Calculator
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Law of cosine calculator or cosine law calculator applies the laws of cosine 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.

There are two calculator below, one is for SAS and another calculator is for SSS. In case of SAS, default first and second side length and angle is given. It will calculate the third side length when u click "Find Third Side Length". In case of SSS, default first, second and third side length is given. It will calculate the angle of the triangle when u click "Find Angle".
 

Steps for finding unknown values using Laws of Cosines

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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 SSS (Side side side) theorem and uses sine laws for calculating the unknown values for finding the angles. For sides it is same as SAS (side angle side) theorem.



Example Problems on Laws of Cosines

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  1. Find the value of a when A = 50°, c = 25 and b = 14.


    Step 1 :  

    Cosin law: a2 = b2 + c2 - 2bc cos A
    a2 = 142 + 252 - 2 x 14 x 25 x cos50°



    Step 2 :  

    a2 = 196 + 625 - 700(0.6427)
    a2 = 371.11



    Answer  :  

    Therefore, a = 19.26, which is equal to 19



  2. Find length of largest diagonal of a parallelogram to its nearest integer whose sides of adjacent are c = 45, a = 25cms and its largest parallelogram angle is B = 115°.


    Step 1 :  

    Cosine law: b2 = a2 + c2 - 2ac cos B
    b2 = 252 + 452 - 2 x 25 x 45 x cos115



    Step 2 :  

    b2 = 625 + 2025 - 2250 x (-0.4226)
    Here, the cosin of obtuse angle is getting negative so the last term changes its sign.
    b2 = 2650 - 2250(-0.4226)
    b2 = 2650 + 950.85
    b2 = 3600.85



    Answer  :  

    Therefore, b = 60



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