8.2 - Trig - Finding Sides

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 when given the lengths of the other two sides?

Back

Use the Pythagorean theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the other sides.

Front

What is the sine function in relation to a right triangle?

Back

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

Front

What is the cosine function in relation to a right triangle?

Back

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

Front

What is the tangent function in relation to a right triangle?

Back

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

Front

How do you calculate the length of a side using the sine function?

Back

To find the length of the opposite side, use the formula: opposite = hypotenuse × sin(θ). To find the hypotenuse, use: hypotenuse = opposite/sin(θ).

Front

How do you calculate the length of a side using the cosine function?

Back

To find the length of the adjacent side, use the formula: adjacent = hypotenuse × cos(θ). To find the hypotenuse, use: hypotenuse = adjacent/cos(θ).

Front

How do you calculate the length of a side using the tangent function?

Back

To find the length of the opposite side, use the formula: opposite = adjacent × tan(θ). To find the adjacent side, use: adjacent = opposite/tan(θ).

Front

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

Back

In a right triangle, the angles determine the ratios of the lengths of the sides. The larger the angle, the longer the opposite side relative to the adjacent side.

Front

What is the significance of rounding in trigonometric calculations?

Back

Rounding is important in trigonometric calculations to ensure that answers are presented in a manageable form, especially when dealing with real-world measurements.