How to Calculate the Area of a Triangle Using the Sine

The area of a triangle is normally calculated as the product of a value equal to one half the measure of the base and the height of the triangle. While this formula is arguably the most commonly reported means of calculating area, there are instances in which the height of a triangle is not known. Instead, two adjacent sides of a triangle and the measure of the resulting angle may be used to determine the area using the sine function.

Things You'll Need

  • Scientific calculator
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Instructions

    • 1

      Identify the length of two adjacent sides of a triangle and the measure of the respective angle at their intersection point. For example, assume a triangle has two adjacent sides measuring 3 and 4 inches respectively and form an angle measuring 45 degrees.

    • 2

      Substitute the observed values into the area formula for a triangle. Area = 1/2 (a)*(b)*sin(c), where a and b are the lengths of the two sides and c is the measure of the angle.

    • 3

      Plug the equation into a scientific calculator to identify the area of the triangle. In the example problem, plugging the values into a calculator results in an area of 4.2 square inches: 1/2*(4)*(3)* sin(45) = 4.2 inches^2.

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