SAT Math: Right Triangles and Trigonometry Flashcards

Question 1

What is Hypotenuse?

Accepted Answer

The longest side of a right triangle, always lying directly across from the 90° angle and never touching it.

Question 2

Define Legs of a Right Triangle.

Accepted Answer

The two shorter sides of a right triangle, which meet to form the 90° angle and serve as base and height for its area.

Question 3

Define Pythagorean Theorem.

Accepted Answer

In every right triangle, the squares of the two shorter sides add up to the square of the longest side: a² + b² = c².

Question 4

Define Converse of the Pythagorean Theorem.

Accepted Answer

Working backwards from the theorem: any three lengths that obey the sum-of-squares rule build a triangle with a 90° corner facing its longest edge.

Question 5

Define Pythagorean Triples.

Accepted Answer

Whole-number side lengths that fit a² + b² = c² exactly; the SAT favours 3-4-5, 5-12-13, 8-15-17 and 7-24-25.

Question 6

Define Scaled Triples.

Accepted Answer

Multiplying every side of a Pythagorean triple by the same number gives another right triangle with identical angles.

Question 7

Define 45-45-90 Triangle.

Accepted Answer

The special right triangle with two equal legs; written as a ratio its sides are x : x : x√2, the longest being √2 times either shorter one.

Question 8

Define 30-60-90 Triangle.

Accepted Answer

A right triangle whose sides follow the ratio x : x√3 : 2x, with the shortest side opposite 30° and the hypotenuse twice that shortest side.

Question 9

Define Opposite Side.

Accepted Answer

Relative to a chosen acute angle, the leg that lies across from it rather than forming one of its arms.

Question 10

Define Adjacent Side.

Accepted Answer

Relative to a chosen acute angle, the leg that forms one of its arms alongside the hypotenuse.

Question 11

What is Sine?

Accepted Answer

For an acute angle in a right triangle, the ratio of the length of the side across from the angle to the length of the hypotenuse.

Question 12

What is Cosine?

Accepted Answer

For an acute angle in a right triangle, the ratio of the leg touching the angle to the length of the hypotenuse.

Question 13

What is Tangent?

Accepted Answer

For an acute angle in a right triangle, the ratio of the side across from the angle to the side touching it.

Question 14

What is SOHCAHTOA?

Accepted Answer

A memory aid for the three basic ratios: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.

Question 15

Define Sine and Cosine of Complementary Angles.

Accepted Answer

For any acute angle x, sin x = cos(90° − x), because the leg across from one acute angle is the leg next to the other.

Question 16

Define Trig Ratios Depend Only on the Angle.

Accepted Answer

Because all right triangles with the same acute angle are similar, a ratio such as sin 40° has one fixed value however large the triangle is.

Question 17

Define Angle of Elevation.

Accepted Answer

The angle between the horizontal and an observer's line of sight looking up at an object above eye level.

Question 18

Define Angle of Depression.

Accepted Answer

The angle between the horizontal and an observer's line of sight looking down at an object below eye level.

Question 19

Define Similar Triangles.

Accepted Answer

Triangles with all three angles equal, so their sides are in proportion and one is a scaled copy of the other.

Question 20

Define Scale Factor.

Accepted Answer

The constant ratio between matching sides of two similar figures; lengths multiply by it, while areas multiply by its square.

Question 21

Define Triangle Angle Sum.

Accepted Answer

The interior angles of every triangle total 180°, so the two acute angles of a right triangle always total 90°.

Question 22

What is Radian?

Accepted Answer

A unit of angle in which one full turn is 2π, so a straight angle of 180° measures π radians.

Question 23

Define Converting Degrees and Radians.

Accepted Answer

To change degrees into radians multiply by π/180, and to change radians into degrees multiply by 180/π.

Question 24

Define Unit Circle.

Accepted Answer

A circle of radius 1 centred at the origin; the point reached by turning angle θ from the positive x-axis has coordinates (cos θ, sin θ).

Question 25

Define Diagonal of a Square.

Accepted Answer

The line joining opposite corners of a square, always √2 times as long as one side, because it is the hypotenuse of a half-square isosceles right triangle.

Question 26

Define Height of an Equilateral Triangle.

Accepted Answer

Dropping a height splits an equilateral triangle into two 30-60-90 triangles, so the height is the side length times √3 ÷ 2.

Question 27

Define Area of a Right Triangle.

Accepted Answer

Half the product of the two legs, since the legs meet at 90° and so act as the base and the perpendicular height.

Question 28

Define Isosceles Right Triangle.

Accepted Answer

A right triangle with two equal legs; its two acute angles are both 45°, making it the 45-45-90 special triangle.