M4 Final Assessment: Trig Ratios, Pythagorean Theorem

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: a² + b² = c².

Front

How do you determine if a set of numbers can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the Pythagorean Theorem holds true: a² + b² = c², where c is the longest side.

Front

What is a trigonometric ratio?

Back

A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).

Front

What is the sine of an angle in a right triangle?

Back

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

Front

What is the cosine of an angle in a right triangle?

Back

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

Front

What is the tangent of an angle in a right triangle?

Back

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

Front

How do you find the height of an object using trigonometry?

Back

To find the height of an object, use the formula: height = distance from the object * tan(angle of elevation).

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. The side opposite the 30° angle is the shortest.

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

What is the formula for the diagonal of a rectangle?

Back

The diagonal (d) of a rectangle can be found using the Pythagorean Theorem: d = √(length² + width²).