Right Triangles Review Support

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

How do you find the distance between two points using the Pythagorean Theorem?

Back

To find the distance between two points (x1, y1) and (x2, y2), use the formula: Distance = √((x2 - x1)² + (y2 - y1)²). This represents the hypotenuse of a right triangle formed by the horizontal and vertical distances.

Front

What is the sine of an angle in a right triangle?

Back

The sine of an angle (θ) is the ratio of the length of the opposite side to the length of the hypotenuse. Formula: sin(θ) = Opposite/Hypotenuse.

Front

What is the cosine of an angle in a right triangle?

Back

The cosine of an angle (θ) is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: cos(θ) = Adjacent/Hypotenuse.

Front

What is the tangent of an angle in a right triangle?

Back

The tangent of an angle (θ) is the ratio of the length of the opposite side to the length of the adjacent side. Formula: tan(θ) = Opposite/Adjacent.

Front

If sinA = 15/17, what is cosA?

Back

Using the Pythagorean identity sin²A + cos²A = 1, we can find cosA. If sinA = 15/17, then cosA = √(1 - (15/17)²) = 8/17.

Front

What is the relationship between sine and cosine?

Back

Sine and cosine are related through the Pythagorean identity: sin²(θ) + cos²(θ) = 1. They are also complementary: sin(θ) = cos(90° - θ).

Front

How do you solve for a missing angle in a right triangle?

Back

To solve for a missing angle, use the inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹, depending on the known sides. For example, if you know the opposite and adjacent sides, use tan⁻¹(Opposite/Adjacent).

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1. This means that for any angle, the sine value will always fall within this interval.

Front

What is the range of the cosine function?

Back

The range of the cosine function is also from -1 to 1, similar to the sine function.