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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

An equilateral triangle is a triangle in which all three sides are equal.

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An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant ... 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

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... more

The area of a regular inscribed n-gon (polygon) can be computed in terms of the radius R of its circumscribed circle and its perimeter p

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In mathematics, the Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides 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/

Relates the projection of a median and the sides of an arbitrary triangle

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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

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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 by20 degrees, then the objects in the map will correspondingly rotate20 degreesclockwise. Find the new coordinates of the character.