help me please

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find the area of each triangle to the nearest tenth.

in triangle YZX x=12cm z=16cm measure of angle Y= 130 degrees

in trianglE XYZ z= 11in. x= 7in. y= 13in.

  • geometry -

    Use this formula, which is attributed to Heron of Alexandria but can be traced back to Archimedes.

    Area = sqrt[s(s-a)(s-b)(s-c)],

    where s=(a+b+c)/2 or perimeter/2.

  • help me please -

    To use that formula on the first triangle, you need to figure the length of side y

    Draw the altitude h from Y to XZ, meeting XZ at P
    Let angle a = <XYP

    h/16 = cos a
    h/12 = cos(130-a)

    16cos z = 12cos(130-a)
    a = 68.81°

    So, side y = XZ = 16sin68.81° + 12sin61.19° = 25.432

    Now you can use Heron's formula to find the area: 73.54

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