Same Math › Geometry · grades 9–10 › SOH CAH TOA
What does SOH CAH TOA mean?
SOH CAH TOA is how kids remember the three trig ratios in a right triangle. Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent. First label the sides from the angle's point of view, pick the ratio that uses the two sides you have, then solve with a calculator.
- Opposite: across from the angle.
- Adjacent: next to the angle (not the hypotenuse).
- Hypotenuse: the longest side, across from the right angle.
Why schools teach it
Finding sides and angles without measuring
Geometry students learn that the ratios of sides in a right triangle depend only on the angle (HSG.SRT.C.6) and use them to solve right triangles (HSG.SRT.C.8): ramps, ladders, heights of buildings.
Labeling first is the whole trick. Opposite and adjacent change when you switch angles, so kids relabel every time.
At the kitchen table
What to say, and what to skip
Say this
Which angle are we using?
Label from there.Which two sides do you know or need?
That picks the ratio.Is your calculator in degree mode?
To find an angle, which button?
sin⁻¹, cos⁻¹ or tan⁻¹.
Skip this
- Calling the hypotenuse “adjacent.”It's always the hypotenuse.
- Radians mode on the calculator.Check for DEG. A wrong mode gives wild answers.
- Using SOH CAH TOA on a triangle without a right angle.It only works on right triangles.
See it in action
Finding x when the angle is 35°, the hypotenuse is 10 and x is opposite
Opposite and hypotenuse: SOH
sin 35° = x/10Multiply both sides by 10
x = 10 · sin 35°Calculate and round
x ≈ 5.7
If x were the hypotenuse, it would end up in the denominator: x = 10 ÷ sin 35°.
Free practice sheet
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Parents: tell your child's teacher about this guide
Parents also ask
What does sin⁻¹ mean?
Inverse sine: give it a ratio, and it gives back the angle.
Do kids need to memorize values?
Not usually in Geometry; they use a calculator. 30°, 45° and 60° values come later.
What if x ends up on the bottom?
Multiply both sides by x, then divide: 10 = x · sin 35° means x = 10 ÷ sin 35°.
Are there other memory tricks?
Some classes use “Oscar Had A Heap Of Apples.” SOH CAH TOA is the most common.