Use the Pythagorean theorem, special right triangles, sine, cosine and tangent, and radian measure. It is part of Geometry and Trigonometry in the Math section. The book teaches it in Chapter 27, Right Triangles and Trigonometry, with 16 practice questions, and tests it 4 more times across the two full-length practice tests.
About Chapter 27
This chapter covers the Pythagorean theorem, the two special right triangles on the reference sheet, and the three trigonometric ratios. Every question here rests on one picture: a right triangle whose sides are named from the point of view of one angle. Once you can label that picture quickly, most of these questions become a single equation.
What the question looks like
Find a missing side when two sides are known: a ladder against a wall, a diagonal brace, a ramp, or the distance between two points.
Use a 30°-60°-90° or 45°-45°-90° triangle, often hidden inside a square, an equilateral triangle or a rectangle.
Find a ratio such as sin A or tan B from side lengths, or find one ratio from another.
Find a side or an angle in a real setting, such as the rise of a ramp or the height reached by a crane.
Use the complementary-angle relationship: sin x° = cos y°, and you need x + y or one of the values.
Compare similar right triangles, whose matching angles have equal trigonometric ratios.
Answer choices often contain radicals, such as 6√3, or exact fractions, such as 20/29.
How to recognize it
A right angle and two known sides: Pythagorean theorem
A 30°, 45° or 60° angle, a square's diagonal, or an equilateral triangle's height: Special right triangles
sin, cos or tan in the stem, or an angle of elevation or incline: SOH-CAH-TOA
Sine on one side of an equation and cosine on the other: Complementary angles
"Triangle DEF is similar to triangle ABC" plus a ratio: Ratios carry over to matching angles
Two points in the xy-plane and the word "distance": Pythagorean theorem on the horizontal and vertical gaps
Common traps
Using the wrong side as the hypotenuse: The hypotenuse is across from the right angle and is the longest side
Swapping opposite and adjacent: Label the sides from the angle named in the question
Mixing up the 30°-60°-90° legs: The short leg is opposite the 30° angle
Dividing by 2 instead of √2: You are going from a 45°-45°-90° hypotenuse to a leg
A calculator in radian mode: A negative or strange value for an acute angle
Setting the angles in sin a° = cos b° equal: Sine and cosine on opposite sides mean the angles add to 90
Adding squares to find a leg: The unknown side is not the hypotenuse, so subtract
Video lessons
Two short lessons from independent YouTube creators, chosen for this skill. The notes are ours; the videos belong to their creators, who are not affiliated with this site.
Right-triangle trigonometry (Settele Tutoring — SAT® Lessons and Strategies, 6:22). Watch for: SOH-CAH-TOA and the sine-cosine complement rule.
How special right triangles work (Does Math for Coffee, 6:44, captions). Watch for: The 45-45-90 and 30-60-90 side ratios.
Practice this skill
The full method, worked examples and 16 practice questions with every answer choice explained are in Chapter 27 of the book and in the study workspace, where an AI coach can talk you through each one.
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