Pythagorean Theorem/Trigonometry

Front

What is the Pythagorean Theorem?

Back

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

Define sine (sin) in a right triangle.

Back

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

Front

Define cosine (cos) in a right triangle.

Back

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

Front

Define tangent (tan) in a right triangle.

Back

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

Front

What is the relationship between sine and cosine for complementary angles?

Back

For any angle θ, sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ).

Front

How do you find the hypotenuse in a right triangle?

Back

Use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

What is the angle of elevation?

Back

The angle of elevation is the angle formed by the line of sight when looking up from a horizontal line to an object above.

Front

How do you calculate the angle of elevation using tangent?

Back

Use the formula: tan(θ) = opposite/adjacent. Rearranging gives θ = arctan(opposite/adjacent).

Front

What is the sine rule in trigonometry?

Back

In any triangle, the ratio of a side length to the sine of its opposite angle is constant. Formula: a/sin(A) = b/sin(B) = c/sin(C).

Front

What is the cosine rule in trigonometry?

Back

In any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle. Formula: c² = a² + b² - 2ab*cos(C).