The law of sines is a / sin A = b / sin B = c / sin C. Each side sits over the sine of the angle opposite it. Use it when the triangle is not a right triangle, or when you have an angle and the side across from it. Right-triangle ratios stay in SOH-CAH-TOA.
Match opposite pairs
If angle A is 40°, side a is 10, and angle B is 60°, then 10 / sin 40° = b / sin 60°. Cross-multiply for b. You need a calculator or Desmos for the sines unless the angles are 30, 45, or 60. Special right triangles are in special right triangles.
Triangle problems that are not this formula are in triangle problems. The formula list is in ACT Math formulas.
The bottom line
Pair each side with the angle across from it. Set two of those fractions equal and solve. Do not use SOH-CAH-TOA unless you have a right angle.
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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