Area of a triangle – Given two sides and an included angle

Area of a triangle – Given two sides and an included angle

Understanding the Area of a Triangle Given Two Sides and an Included Angle

  • An included angle in a triangle is the angle formed between two given sides.
  • The formula used to find the area of a triangle given two sides and an included angle is different from the usual base times height method.
  • This advanced formula is based on trigonometry and is particularly useful for triangles where the height is unknown or difficult to measure.

The Formula

  • The formula is: Area = 0.5abSinC.
  • In this formula, a and b represent the lengths of the two sides of the triangle, and C represents the included angle.
  • It’s important to note that the angle must be in degrees for the formula to work correctly.

Applying The Formula

  • To calculate the area, multiply the lengths of the two sides of the triangle and the sine of the included angle.
  • Then multiply the result by 0.5 (or divide it by 2) to get the final area.
  • The sine (Sin) of an angle can be found using a scientific calculator. Make sure your calculator is set to degrees, not radians.
  • Always remember to state your answers with the correct units of measurement. If you are given measurements in metres, your answer should be in square metres.

Understanding Sine

  • The term sine comes from trigonometry, a branch of mathematics that studies the relationships between the angles and sides of triangles.
  • In a right-angled triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
  • While a basic grasp of trigonometry can be helpful for understanding the area formula, all you really need to know is how to use your calculator to find the sine of an angle.

Revision and Practice

  • Understand that mastery of this method requires consistent practice.
  • Work through a variety of problems with different triangle shapes and measurements to strengthen your understanding.
  • Regular revision of these concepts will ensure maximum retention and recall during your assessments.