The Pythagorean theorem, special right triangles, and SOH-CAH-TOA trigonometric ratios, including the sine-cosine complement relationship.
48
Total questions
22
Easy
12
Medium
14
Hard
Expect the Pythagorean theorem, the special right triangles (45-45-90 and 30-60-90, both on the reference sheet), and the three basic trig ratios. A recurring SAT favorite: sin(x°) = cos(90° − x°), the complementary-angle identity, often dressed up algebraically.
Label the triangle from the angle you're working with — opposite, adjacent, hypotenuse shift when the angle changes. Recognize Pythagorean triples (3-4-5, 5-12-13 and their multiples) to skip computation. When two acute angles of right triangles have sines and cosines set equal, reach for the complement identity before anything else.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: A
Choice A is correct. Using the Pythagorean theorem: 7² + 24² = c², so 49 + 576 = c², or 625 = c². Taking the square root yields c = 25. Choice B is incorrect (24 - 7). Choice C is incorrect (24 + 7). Choice D is incorrect (this is c², not c).
Correct answer: B
Choice B is correct. If tan(M) = 7/24, the opposite side is 7 and the adjacent side is 24 (or proportional). The hypotenuse = √(7² + 24²) = √(49 + 576) = √625 = 25. Therefore, sin(M) = opposite/hypotenuse = 7/25. Choice A is incorrect (this is tan(M)). Choice C is incorrect (this is cos(M)). Choice D is incorrect.
Area & Volume
Areas of 2D figures and volumes of 3D solids, including composite shapes and problems where scaling changes area or volume.
Lines, Angles & Triangles
Parallel-line angle relationships, triangle angle sums, similarity and congruence, and the triangle inequality.
Circles
Circle equations in the xy-plane, arc length, sector area, central angles, and completing the square to find center and radius.
48 Right Triangles & Trigonometry questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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