Pythagoras & Trigonometry Revision

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). It can be expressed as: c² = a² + b².

Front

How do you find the length of a side in a right triangle using the Pythagorean theorem?

Back

To find the length of a side in a right triangle, rearrange the Pythagorean theorem formula. For example, to find side a: a = √(c² - b²).

Front

What is the sine function in trigonometry?

Back

The sine function (sin) is a ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. It is defined as: sin(θ) = opposite/hypotenuse.

Front

What is the cosine function in trigonometry?

Back

The cosine function (cos) is a ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is defined as: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent function in trigonometry?

Back

The tangent function (tan) is a ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is defined as: tan(θ) = opposite/adjacent.

Front

How do you calculate the length of the hypotenuse?

Back

To calculate the length of the hypotenuse in a right triangle, use the Pythagorean theorem: c = √(a² + b²).

Front

What is the relationship between the angles and sides in a right triangle?

Back

In a right triangle, the angles are related to the sides through trigonometric ratios. The larger the angle, the longer the opposite side relative to the adjacent side.

Front

How do you find the angle using trigonometric ratios?

Back

To find an angle in a right triangle, use the inverse trigonometric functions: θ = sin⁻¹(opposite/hypotenuse), θ = cos⁻¹(adjacent/hypotenuse), or θ = tan⁻¹(opposite/adjacent).

Front

What is the significance of rounding answers in geometry problems?

Back

Rounding answers in geometry problems is important for precision and clarity. It helps to present answers in a manageable form, especially when dealing with measurements.

Front

What is the formula for finding the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) × base × height.