SAT Math: Trigonometric Ratios (SOH-CAH-TOA)
36+ practice questions in Praczo
The concept, explained
- 1
In a right triangle, for acute angle θ: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Mnemonic: SOH-CAH-TOA.
- 2
"Opposite" and "adjacent" are relative to the angle θ — they change depending on which angle you choose. The hypotenuse never changes.
- 3
To find a missing side: set up the ratio, write the equation, and solve. sin(30°) = x/10 → x = 10 sin(30°) = 5.
- 4
Cofunction identity: sin θ = cos(90° − θ). In a right triangle, sin of one acute angle equals cos of the other.
- 5
If sin A = cos B, then A + B = 90°. The SAT tests this identity directly.
- ✗ Mixing up opposite and adjacent. Always label sides relative to the specific angle in use, not a different angle.
- ✗ Forgetting the cofunction identity: sin(40°) = cos(50°). If the SAT writes sin A = cos B, then A + B = 90°.
SAT-style practice
In a right triangle, angle A measures 35°, the hypotenuse is 20, and the side opposite angle A is x. Which equation can be used to find x?
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