Using the Trigonometry Formula - SOH-CAH-TOA

What is SOHCAHTOA and how to use the trig ratios to find missing sides and missing angles on right triangles?

The following diagram shows the SOHCAHTOA formula for sin, cos, and tan. Scroll down the page for more examples and solutions on SOHCAHTOA.

 

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What is SOH-CAH-TOA?
SOHCAHTOA is a mnemonic to help us remember the trigonometric ratios.
Sine = Opposite/Hypotenuse (SOH)
Cosine = Adjacent/Hypotenuse (CAH)
Tangent = Opposite/Adjacent (TOA)

How to Use SOHCAHTOA:

1. Identify the angle you are working with.
   
2. Label the sides of the triangle as hypotenuse, opposite, and adjacent relative to that angle.
3. Determine which trigonometric function (sine, cosine, or tangent) relates the sides you know or the side you need to find. Use SOHCAHTOA to help you choose.
4. Set up the equation using the appropriate ratio.
5. Solve for the unknown side length or angle. You may need to use a calculator to find the sine, cosine, or tangent of an angle, or the inverse trigonometric functions (arcsin, arccos, arctan) to find an angle.

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Basic Trigonometry Formula - SOH-CAH-TOA
A basic introduction to defining the three major trigonometric functions (sine, cosine, tangent) are discussed using the mnemonic SOH-CAH-TOA.

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Basic Trigonometry Review - SOH-CAH-TOA
A review of basic trigonometry: Sine, Cosine & Tangent including how to use the ratios to find missing sides and missing angles on right triangles.

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Sine Cosine Tangent - SOHCAHTOA
Students learn that the sine of an angle of a right triangle is equal to the length of the side opposite the angle over the length of the hypotenuse (SOH), the cosine of an angle of a right triangle is equal to the length of the side adjacent to the angle over the length of the hypotenuse (CAH), and the tangent of an angle of a right triangle is equal to the length of the side opposite the angle over the length of the side adjacent to the angle (TOA).

Students are then asked to find the values of the sine, cosine, and tangent of given angles in given right triangles.

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Common Mistakes to Avoid
❌ Mislabeling sides: Ensure “adjacent” is next to θ (not the hypotenuse).
❌ Using the wrong ratio: Match the sides you have to SOH-CAH-TOA.
❌ Calculator mode: Always check if your calculator is in degrees (DEG) for angles.

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