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Introduction to Trigonometry: sub-module 6 of 6 of math tutorials

Have you ever wondered how the heights of very tall objects like mountains are measured? The measurement process involves the use of triangles and a branch of mathematics known as trigonometry. In this module, we will review angles, triangles, and right-triangle trigonometry, including the Pythagorean theorem and the primary trigonometric ratios.


Top Tips


  • Complementary angles sum to 90° and supplementary angles sum to 180°. To help you remember this, note that complementary and supplementary are in alphabetical order just like 90° and 180° are in numerical order.
  • Right triangles contain one angle that is exactly 90°. The side opposite the right angle is the longest side and is called the hypotenuse, and the two shorter sides are called legs.
  • The interior angles of any triangle sum to 180°. If you add all the angles of triangle it will equal 180°. This is true for ALL triangles.
  • Similar triangles have all the same angles but are different sizes. In similar triangles, the ratios of corresponding sides are all the same and corresponding angles have the same measure.
  • The Pythagorean theorem and the trigonometric ratios ONLY work for right triangles. Remember that you can only use the Pythagorean theorem and the sine, cosine, and tangent ratios if you have a right triangle.
  • Use the memory aid SOHCAHTOA to remember your primary trigonometric ratios. The Sine is the Opposite side over the Hypotenuse, the Cosine is the Adjacent side over the Hypotenuse, and the Tangent is the Opposite side over the Adjacent side.
  • Check that your calculator is set to the correct unit of measure for angles. Degrees are a commonly used unit of measure for angles, but you may also use radians or gradients. Make sure you check that your calculator is in the unit of measure you are working with before you do any calculations.