Trigonometry - Part 1

Front

What is the definition of a triangle's area?

Back

The area of a triangle is defined as the amount of space enclosed within its three sides, calculated using the formula: Area = 1/2 * base * height.

Front

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

Back

In a right triangle, the Pythagorean theorem states that 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): c² = a² + b².

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

What does it mean to round a number to the nearest tenth?

Back

Rounding a number to the nearest tenth means adjusting the number to one decimal place, where if the digit in the hundredths place is 5 or greater, you round up, and if it is less than 5, you round down.

Front

How do you calculate the area of a triangle given two sides and the included angle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * a * b * sin(C), where a and b are the lengths of the two sides and C is the included angle.

Front

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

Back

In any triangle, the larger the angle, the longer the opposite side. This is known as the triangle inequality theorem.

Front

What is the significance of the 30-60-90 triangle?

Back

In a 30-60-90 triangle, the sides are in a specific ratio: the side opposite the 30° angle is half the hypotenuse, the side opposite the 60° angle is √3/2 times the hypotenuse.

Front

What is the significance of the 45-45-90 triangle?

Back

In a 45-45-90 triangle, the sides are in a specific ratio: both legs are of equal length, and the hypotenuse is √2 times the length of each leg.