MathRight Triangles and TrigonometryHigh frequency
SAT Math: Use trig ratios to find a missing side
25+ practice questions in Praczo
What you need to know
The concept, explained
- 1
SOH-CAH-TOA: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
- 2
Identify the known angle and its known side, then pick the ratio that involves the unknown side.
- 3
To solve, set up the ratio and isolate the unknown: if sin 30° = x/10, then x = 10 · sin 30°.
- 4
Use your calculator in degree mode unless radians are specified. Check the mode before computing.
Common mistakes
- ✗ Using the wrong trig ratio — double-check which side is opposite, adjacent, or hypotenuse relative to the known angle.
- ✗ Having the calculator in radian mode when the angle is in degrees (or vice versa).
Try a sample question
SAT-style practice
In a right triangle, one angle measures 30° and the hypotenuse is 20. What is the length of the side opposite the 30° angle?
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