Answer all the questions below and press submit to see how many you got right.
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≤α≤180∘ or cosα is defined by finding a right triangle with angle α and dividing the length of the leg adjacent to α 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 cos2α+sin2α=1.
Cot : In a right triangle with one of the angles adjacent to the hypotenuse being equal to α, cotα is defined as the length of the leg adjacent to the angle divided by the length of the other leg. We have cotα=1tanα=cosαsinα.
Fraction : A fraction is a number that can be written as ab with an integer a and a natural numbers b. A fraction ab is the result of the division a÷b. Examples of fractions are 12,−23 and 32.
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≤α≤180∘ or sinα is defined by finding a right triangle with angle α and dividing the length of the leg opposite to α 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 cos2α+sin2α=1.
Tan : The tangent of an angle 0≤α≤180∘ or tanα is defined by finding a right triangle with angle α and dividing the length of the leg opposite to α by the length of the leg adjacent to α. 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 tanα=sinαcosα.
Trigonometric function : Trigonometric functions are the functions commonly used in trigonometry like sinx, cosx, tanx, cotx and their inverse functions arcsinx, arccosx, and arctanx.
Given is a right triangle that has a hypotenuse of length c. One of the other angles is α and the leg opposite to this angle has length a. Then ac=?
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.
Congruent triangle : Two triangles are called congruent if they have the same shape and size.
Division : Division is the mathematical operation that divides objects equally into groups. More generally x÷y is defined as the number that if multiplied by y equals x.
Equilateral triangle : An equilateral triangle is a triangle with three sides of equal length. An equilateral triangle is also equiangular and has interior angles of 60∘.
Half : A Half is the number equal to 12=0.5.
Height : In a triangle a height (or altitude) is the shortest line segment that connects a side to its opposing corner. A height of a triangle is perpendicular to the side is started at. The three heights of a triangle intersect in a point, the so called orthocenter of the triangle. In a parallelogram the height is the shortest distance between two opposing sides. In a pyramid the height is the shortest distance between the base area and the corner of the pyramid that is not part of the base area. In a prism the height is the shortest distance between the two base faces.
Pythagorean theorem : The Pythagorean theorem states that in a right triangle the square of the hypotenuse c2 equals the sum of the squares of the legs a2+b2. It can be used to calculate the length of a third side of a right triangle given the other two. It also can be used to calculate the lengths of diagonals in rectangles or cubes.
Square root : The square root of x denoted by √x is the positive number such that (√x)2=√x⋅√x=x. For example √9=3.
Square root of 2 : The square root of 2 also written as √2 is the positive number such that (√2)2=√2⋅√2=2. √2 is an irrational number and rounded to the nearest hundredths it is equal to 1.41.
Square root of 3 : The square root of 3 also written as √3 is the positive number such that (√3)2=√3⋅√3=3. √3 is an irrational number and rounded to the nearest hundredths it is equal to 1.73.
Squared : x squared refers to the number x2=x⋅x. For example 3 squared equals 9.
Third : A third either refers to the third object in an ordering or to the number 13=0.¯3.
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∘.
We are given an equilateral triangle with side lengths 1. Lets denote the height of that triangle by h. The height divides the triangle into two congruent right triangles with angles 30∘ and 60∘, hypotenuse 1 and side lengths 0.5 and h. This implies sin60∘=cos30∘=h1=h. What is the height of the equilateral triangle h?
Circle : A circle is a two-dimensional shape. The boundary of a circle is a set of points that has the same distance (the radius) from the center of the circle.
Tangent : A tangent is a line that touches a curve or a surface at one point without going through the curve or surface.
What is the length of the tangent d in the picture?