SOHCAHTOA on the SAT

Why the SAT Emphasizes SOHCAHTOA

SOHCAHTOA is the shortcut for right triangle trigonometry. The SAT uses it to test whether you can choose the correct ratio based on a labeled diagram.

In this lesson, you will practice labeling opposite, adjacent, and hypotenuse relative to the given angle, then selecting the ratio that matches the known and unknown sides.

A Simple Definition Unlocks SOHCAHTOA

Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. These ratios only make sense after you label the sides relative to the angle you care about.

The most common mistake is labeling the sides relative to the wrong angle. Always circle the given angle first, then label the opposite and adjacent sides from that point of view.

Work Through SOHCAHTOA Step by Step

Work through a simple right triangle so you see how the sine ratio uses opposite and hypotenuse.

Use Desmos to Check SOHCAHTOA

Desmos can evaluate trig ratios quickly if you need a decimal. It is especially useful when the question provides an angle and asks for an approximate value.

Exact ratios are usually better for SAT multiple choice, but Desmos can check your work.

Desmos is faster when the angle is not a special angle and you only need a decimal. Algebra and exact ratios are faster when the angle is $30^\circ$, $45^\circ$, or $60^\circ$ and the problem expects radicals.

Expert move: Use Desmos to evaluate trig ratios or inverse trig when the angle is not special; keep exact values when possible and check the quadrant/sign.

• Desmos features used: trig evaluation.
• Common mistake: mixing up opposite and adjacent.

Practice SOHCAHTOA with SAT-Style Questions

Choose the correct ratio for each situation.

Key Takeaways to Remember for SOHCAHTOA

• Label opposite, adjacent, and hypotenuse relative to the angle.
• Use SOHCAHTOA to choose the correct ratio.
• Desmos can provide decimal checks if needed.