Free SAT SOH-CAH-TOA Mock Test

Got tangled up in triangles and trigonometry? Master SAT - SOHCAHTOA fast! Take a quick SAT practice test on Trigonometry to level up your skills, tackle tougher problems, and discover your strengths.

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Right triangles & trigonometry

In a right triangle, the shorter sides measure 12 centimeters (cm) and 16 cm. What is the length, in cm, of the longest side of the triangle?

A 20 B 28 C 40 D 400

Which of the following statement(s) is/are correct about the angle 2π/3 radians?
I. The value of Sin 2π/3 is negative
II. The value of Tan 2π/3 is negative

A Only I B Only II C Both I and II D Neither I nor II

Triangle PQR is similar to triangle XYZ, where P corresponds to X and R corresponds to Z. Angles R and Z are right angles. If sin(P) = 12 and XY = 40, what is the length of XZ?

A 10 B 10/sqrt(3) C 20 D 20/sqrt(3)

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How to solve questions from SOH-CAH-TOA?

Use SOHCAHTOA

Memorize sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent for quick ratio.

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Identify Special Triangles

Recognize 30-60-90 (ratio 1:√3:2) and 45-45-90 (ratio 1:1:√2) triangles to avoid lengthy calculations.

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Pythagorean Theorem

Use a² + b² = c² to find missing sides when two sides are known, then use trig ratios for angles.

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Why SOH-CAH-TOA matter for SAT?

EdisonOS conducted a detailed Bluebook analysis to help tutors design SAT tests mirroring official Bluebook test challenges. Findings show Geometry & Trigonometry occupies the smallest portion of SAT Math, averaging 5 questions. Right triangles and trigonometry shares 2-3 questions making this skill an essential in your study plan

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Avoid These Common Mistakes In SOH-CAH-TOA!

Adjacent/Opposite Side Confusion

Students mix up which side is opposite vs adjacent to the angle, leading to wrong SOHCAHTOA ratios.

Angle Perspective Switching

Students forget that opposite and adjacent sides change when switching between different angles in the triangle

Special Triangle Ratio Errors

Students confuse 30-60-90 and 45-45-90 triangle ratios or apply them to wrong triangle types.

Complementary Angle Mistakes

Students don't recognize that sin(θ) = cos(90° - θ), missing shortcuts in SAT trigonometry problems.

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