Right Triangle Trig: Ratios and Finding Sides

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as: sin(θ) = opposite/hypotenuse.

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as: tan(θ) = opposite/adjacent.

Front

How do you find the length of a side using the sine ratio?

Back

To find the length of a side using the sine ratio, rearrange the formula: sin(θ) = opposite/hypotenuse to find opposite = hypotenuse * sin(θ).

Front

How do you find the length of a side using the cosine ratio?

Back

To find the length of a side using the cosine ratio, rearrange the formula: cos(θ) = adjacent/hypotenuse to find adjacent = hypotenuse * cos(θ).

Front

How do you find the length of a side using the tangent ratio?

Back

To find the length of a side using the tangent ratio, rearrange the formula: tan(θ) = opposite/adjacent to find opposite = adjacent * tan(θ).

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 is expressed as: a² + b² = c².

Front

How do you solve for an unknown side in a right triangle?

Back

To solve for an unknown side, use the appropriate trigonometric ratio (sine, cosine, or tangent) based on the given angle and the sides you know.

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 sides. As one angle increases, the opposite side increases while the adjacent side decreases, maintaining the relationships defined by sine, cosine, and tangent.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for calculating the sine, cosine, and tangent ratios.