Trigonometry

The hypotenuse of a right triangle is 34cm. find the length of the two legs, if one leg is 14cm longer than the other.

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  1. The rule of Pythagoras:

    c ^ 2 = a ^ 12 + b ^ 2

    In this case :

    c = 34 cm

    b = a + 14

    c = a ^ 2 + ( a + 14 ) ^ 2

    34 ^ 2 = a ^ 2 + ( a + 14 ) ^ 2

    1156 = a ^ 2 + a ^ 2 + 2 * a * 14 + 14 ^ 2

    1156 = 2 a ^ 2 + 28 a + 196 Subtract 196 to both sides

    1156 - 196 = 2 a ^ 2 + 28 a + 196 - 196

    960 = 2 a ^ 2 + 28 a Divide both sides by 2

    480 = a ^ 2 + 14 a Add 49 to both sides

    480 + 49 = a ^ 2 + 14 a + 49

    529 = ( a + 7 ) ^ 2

    ________________________________________

    Becouse :

    ( a + 7 ) ^ 2 = a ^ 2 + 2 * a * 7 + 7 ^ 2 =

    a ^ 2 + 14 a + 49

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    sqrt ( 529 ) = sqrt [ ( a + 7 ) ^ 2 ]

    + OR - 23 = a + 7

    1 case:

    23 = a + 7 Subtract 7 to both sides

    23 - 7 = a + 7 - 7

    16 = a

    a = 16 cm

    2 case:

    - 23 = a + 7 Subtract 7 to both sides

    - 23 - 7 = a + 7 - 7

    - 30 = a

    a = - 30 cm

    Length can't be negative so:

    a = 16 cm

    b = a + 14 = 16 + 14 = 30 cm

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