Apply the Pythagorean theorem and basic trigonometric ratios to solve for unknown side lengths.
48 original right triangles and trigonometry questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
In a right triangle, sin(x°) = cos(y°), where x and y are the measures of the two acute angles. If x = 40, what is the value of y?
In a right triangle the two acute angles are complementary, and the sine of an angle equals the cosine of its complement. So x + y = 90, giving y = 90 − 40 = 50. Choice 40 wrongly sets the angles equal.
In a right triangle, angles A and B are the two acute angles, and sin A = cos B. If angle A measures (2x + 10)° and angle B measures (3x − 20)°, what is the value of x?
sin A = cos B holds when A and B are complementary, so 2x + 10 + 3x − 20 = 90. That gives 5x = 100 and x = 20. Choice 30 sets the two expressions equal to each other instead, which would make the angles equal rather than complementary.
In a right triangle, one acute angle measures 30° and the hypotenuse has length 14. What is the length of the side opposite the 30° angle?
In a 30-60-90 triangle the side opposite the 30° angle is half the hypotenuse, so it is 14 ÷ 2 = 7. Choice 7√3 is the side opposite the 60° angle.
In right triangle ABC, the right angle is at C, the hypotenuse AB has length 13, and side BC has length 5. What is the value of sin A?
The sine of an angle is the opposite side over the hypotenuse, and the side opposite angle A is BC = 5, so sin A = 5/13. Choice 12/13 is cos A, using the adjacent side AC = 12.
A right triangle has a leg of length 18 and a hypotenuse of length 30. What is the length of the other leg?
By the Pythagorean theorem: 30² − 18² = 900 − 324 = 576, so the other leg is √576 = 24.