Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.

Hypotenuse : The hypotenuse in a right triangle is the side of the right triangle that does not have any endpoints at the corner with the right angle. The hypotenuse is the longest side in a right triangle and its length can be calculated from the other two side lengths using the Pythagorean theorem.

Leg of a right triangle : A leg of a right triangle is one of the two sides in a right triangle that form the right angle.

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

Right triangle : A right triangle is a triangle that has a right angle. The sides that form the right angle are called legs, the third side is called hypotenuse. The area of a right triangle is half the product of the lengths of the two legs. The Pythagorean theorem is an important theorem for right triangles that allows to calculate the third side of a right triangle given the other two.

Sin : The sine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\sin \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the hypotenuse. For arbitrary angles the sine function can be extended in a periodic way by inscribing the right triangle in a circle. The sine can be used to calculate unknown side lengths in a triangle via the sine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$

Zero : The number 0.

Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.

Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Cot : In a right triangle with one of the angles adjacent to the hypotenuse being equal to $\alpha,$ $\cot \alpha$ is defined as the length of the leg adjacent to the angle divided by the length of the other leg. We have $\cot \alpha= \frac{1}{\tan \alpha} =\frac{\cos \alpha}{\sin \alpha}.$

Fraction : A fraction is a number that can be written as $\frac{a}{b}$ with an integer $a$ and a natural numbers $b.$ A fraction $\frac{a}{b}$ is the result of the division $a\div b.$ Examples of fractions are $\frac{1}{2}, -\frac{2}{3}$ and $\frac{3}{2}.$

Hypotenuse : The hypotenuse in a right triangle is the side of the right triangle that does not have any endpoints at the corner with the right angle. The hypotenuse is the longest side in a right triangle and its length can be calculated from the other two side lengths using the Pythagorean theorem.

Leg of a right triangle : A leg of a right triangle is one of the two sides in a right triangle that form the right angle.

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

Right triangle : A right triangle is a triangle that has a right angle. The sides that form the right angle are called legs, the third side is called hypotenuse. The area of a right triangle is half the product of the lengths of the two legs. The Pythagorean theorem is an important theorem for right triangles that allows to calculate the third side of a right triangle given the other two.

Sin : The sine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\sin \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the hypotenuse. For arbitrary angles the sine function can be extended in a periodic way by inscribing the right triangle in a circle. The sine can be used to calculate unknown side lengths in a triangle via the sine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Tan : The tangent of an angle $0\leq\alpha\leq 180^{\circ}$ or $\tan \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the leg adjacent to $\alpha.$ For arbitrary angles the tangent function can be extended in a periodic way by inscribing the right triangle in a circle. The tangent function can be used to calculate unknown side lengths and angles in right triangles via its definition. We have $\tan \alpha=\frac{\sin \alpha}{\cos \alpha}.$

Trigonometric function : Trigonometric functions are the functions commonly used in trigonometry like $\sin x,$ $\cos x,$ $\tan x,$ $\cot x$ and their inverse functions $\arcsin x,$ $\arccos x,$ and $\arctan x.$

Adjacent : Adjacent means next to each other.

Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.

Congruence : Two shapes are called congruent if they have the same shape and size. Two integers are called congruent modulo $x$ if they have the same remainder in a division by $x.$

Corresponding length : Congruent or similar shapes can be mapped onto each other using translations, reflections, rotations and in the case of similarity dilations. Lengths are called corresponding lengths if they are mapped on top of each other by that mapping.

Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$

Hypotenuse : The hypotenuse in a right triangle is the side of the right triangle that does not have any endpoints at the corner with the right angle. The hypotenuse is the longest side in a right triangle and its length can be calculated from the other two side lengths using the Pythagorean theorem.

Independence : Random variables $X,$ $Y$ are called independent if $P[X\in A, Y\in B]=P[X \in A]P[Y \in B].$ Independent identically distributed random variables feature prominently in the law of large numbers and the central limit theorem. Vectors $x_1,x_2\ldots, x_n$ are called linearly independent if $\lambda_1 x_1+\lambda_2 x_2+\ldots+\lambda_n x_n=0$ implies $\lambda_1=\lambda_2=\ldots=\lambda_n=0.$

Leg of a right triangle : A leg of a right triangle is one of the two sides in a right triangle that form the right angle.

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

Ratio : A ratio is a comparison of two numbers using a division.

Right angle : A right angle is an angle equal to $90^{\circ}.$

Right triangle : A right triangle is a triangle that has a right angle. The sides that form the right angle are called legs, the third side is called hypotenuse. The area of a right triangle is half the product of the lengths of the two legs. The Pythagorean theorem is an important theorem for right triangles that allows to calculate the third side of a right triangle given the other two.

Similar triangle : A similar triangle is a triangle with the same shape but not necessarily the same size. Ratios of corresponding side lengths and corresponding angles are the same in similar triangle. This fact is used to be able to uniquely define the trigonometric functions using ratios of side lengths in right triangles. Two triangles are similar if they share two angles (and therefore all three) or if all 3 ratios of the lengths of corresponding sides in the two triangles are the same. Two triangles are also similar if two ratios of lengths of corresponding sides in the two triangles are the same and the angle between the two sides in the two triangles is the same.

Similarity : Two shapes are called congruent if they have the same shape and size. Corresponding angles are the same in similar shapes and the ratio of corresponding side length is constant.

Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$