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Trigonometry > Finding the Area of a Triangle
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Finding the Area of a Triangle

Main formulas:

  • Master formula for right triangles: SOHCAHTOA!
    sinθ = opposite side

    hypotenuse
        cosθ = adjacent side

    hypotenuse
        tanθ = opposite side

    adjacent side
  • The Law of Cosines (in any triangle):
    c2 = a2 + b2 − 2abcosC
  • Heron's Formula:
    Area =

     

    s(sa)(sb)(sb)
     
    ,
    where s = [1/2](a+b+c) is the semiperimeter of the triangle.

Example 1:

Find the area of a triangle that has two sides of lengths 8 and 12 with an included angle of 45° .

Example 2:

Find the area of a triangle with side lengths 10, 14, and 16.

Example 3:

Without using Heron's formula, find the area of a triangle whose side lengths are 7, 9, and 14.

Example 4:

Find the area of a triangle that has two sides of lengths 7 and 13 with an included angle of 32° .

Example 5:

A triangle has two sides of length 5 and 6 with an included angle of 60° . Find the area of the triangle.
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