The Pythagorean theorem, special right triangles, and SOH-CAH-TOA trigonometric ratios, including the sine-cosine complement relationship.
47
Total questions
22
Easy
12
Medium
13
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. The ramp, the platform's height, and the ground form a right triangle in which the ramp is the hypotenuse, with length 6.5 meters, and the vertical leg is the platform's height, 2.5 meters. By the Pythagorean theorem, the horizontal distance along the ground from the bottom of the ramp to the base of the platform is √(6.5² − 2.5²) = √(42.25 − 6.25) = √36 = 6 meters. For the angle the ramp makes with the ground, the opposite leg is the vertical height, 2.5 meters, and the adjacent leg is the horizontal distance, 6 meters. Therefore, the tangent of this angle is 2.5/6, which is equivalent to 5/12. Choice A is incorrect; 5/13 is the sine of the angle (2.5/6.5), which uses the hypotenuse instead of the horizontal leg. Choice C is incorrect; 12/13 is the cosine of the angle (6/6.5). Choice D is incorrect; 12/5 results from inverting the tangent ratio, dividing the adjacent leg by the opposite leg.
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.
47 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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