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Ceva’s theorem is a theorem about triangles in Euclidean plane geometry. Given a triangle ABC, let the lines AO, BO and CO ... more
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. If the internal ... more
The bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle
... more
Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more
Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the ... more
Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more
Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). Altitude of a triangle is a line ... more
A hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three points called angles or ... more
Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each ... more
Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). Median of a triangle is a line ... more
A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more
A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more
A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more
The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly ... more
Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more
Relates the medians and the sides of an arbitrary triangle. Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. ... more
Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more
Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more
Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more
An equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; ... more
In mathematics, the Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides of ... more
In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle by requiring no ... more
In any convex quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals plus four times the square of ... more
In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle by requiring no ... more
Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more
To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by 20 degrees. To do so, we first need to find the radius of this circle and the original angle.
Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:
To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get
While there are two angles that have this cosine value, the angle of 120.964 degrees is in the second quadrant as desired, so it is the angle we were looking for.
Rotating the point clockwise by 20 degrees, the angle of the point will decrease to 100.964 degrees. We can then evaluate the coordinates of the rotated point
For x axis:
For y axis:
The coordinates of the character on the rotated map will be (-1.109, 5.725)
Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen
http://www.opentextbookstore.com/precalc/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/
Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more
The law of cosines relates the cosine of an angle to the opposite side of an arbitrary triangle and the length of the triangle’s sides.
The law
... more
Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more
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In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates (-3, 5). If the player rotates counterclockwise by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character.