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Trigonometry Help: Understanding SOHCAHTOA

SOHCAHTOA is a mnemonic device for remembering how to calculate the sine, cosine, and tangent of an angle in a right triangle. This article will tell you how to use it and what to do in cases of non-right angled triangles.

SOHCAHTOA Abbreviations

SOHCAHTOA stands for the following:
  • S=Sine=Opposite/Hypotenuse
  • C=Cosine=Adjacent/Hypotenuse
  • T=Tangent=Opposite/Adjacent
Each operation is one side of the triangle divided by another. To calculate the Sine of an angle, divide the length of the side opposite the angle by the length of the hypotenuse. For Cosine, divide the length of the side adjacent to the angle by the hypotenuse. And to find the Tangent, divide the length of the side opposite the angle by the length of the side adjacent. Simple enough? Let's look at an example.

Example 1

Find the sine, cosine, and tangent of angle in the 3-4-5 right triangle above. Let's do the sine first. Sine=Opposite/Hypotenuse. The opposite side is 4 and the hypotenuse is 5. Sine=4/5=0.8. The Cosine=Adjacent/Hypotenuse=3/5=0.6. And the Tangent=Opposite/Adjacent=4/3=1.3 repeating.

Isosceles and Equilateral Triangles

The SOHCAHTOA tool only works with right-angled triangles, so what do you do with a non-right angled triangle? If you have an equilateral or isosceles triangle, you can simply drop a perpendicular line from the apex to the base and form two right triangles. Remember that the apex angle and the base are both bisected.

Other Oblique Triangles

For all other triangles, you must use the Laws of Sine and Cosine. If you know either a) the length of two sides and the angle opposite of one of the sides, or b) two angles and any side, you can use the Law of Sines, which states:  If you know either a) two sides and their shared angle, or b) all three sides, you can use the Law of Cosine. It states that .

For Tutoring in Salem, OR

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