S1 Unit 5: Remediation

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: c² = a² + b².

Front

Define sine (sin) in relation to a right triangle.

Back

Sine is a trigonometric function defined as 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 relation to a right triangle.

Back

Cosine is a trigonometric function defined as 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 relation to a right triangle.

Back

Tangent is a trigonometric function defined as the ratio of the length of the opposite side to the length of the adjacent side. Formula: tan(θ) = opposite/adjacent.

Front

How do you find the angle of elevation?

Back

The angle of elevation can be found using the tangent function: tan(θ) = opposite/adjacent, where 'opposite' is the height and 'adjacent' is the distance from the base.

Front

What is the formula to find the length of a side in a right triangle using trigonometric ratios?

Back

To find a side, use: a = hypotenuse * cos(θ) for adjacent side, or a = hypotenuse * sin(θ) for opposite side.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30-degree angle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

How do you calculate the angle using inverse trigonometric functions?

Back

To find an angle, use: θ = sin⁻¹(opposite/hypotenuse), θ = cos⁻¹(adjacent/hypotenuse), or θ = tan⁻¹(opposite/adjacent).

Front

What is the purpose of using trigonometric ratios in real-life applications?

Back

Trigonometric ratios are used to solve problems involving right triangles, such as calculating heights, distances, and angles in various fields like engineering, architecture, and physics.