SOH-CAH-TOA is the only trig you need for most ACT right triangles: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent. Label the angle you are using, then pick the ratio that matches the two sides you know. The rest of right-triangle trig is in right-triangle trigonometry.
Label first
Opposite is across from the angle. Adjacent is the other leg that touches the angle. Hypotenuse is always across from 90°. If you have opposite and hypotenuse, you want sine. If the question gives you an angle and one side, write the ratio and solve like any proportion.
Special right triangles skip the trig ratios when the angles are 45-45-90 or 30-60-90. Those side lengths are in the Pythagorean theorem and special right triangles.
Two identities that show up
sin²θ + cos²θ = 1, and tan θ = sin θ / cos θ. Those are in the sine-cosine identity. The formula list is in ACT Math formulas.
The bottom line
Mark the angle, name opposite, adjacent, and hypotenuse, then write the one ratio you need.
Start practicing
Start with a free diagnostic, then drill your weak spots with 15-question quizzes and track how you're doing across Reading, English, and Math. Compare plans whenever you're ready to go further.
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