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On 2-D displays, such as computer monitors and TVs, the display size (or viewable image size or VIS) is the physical size of the ... more

The inradius (the radius of the incircle of the rhombus) can be expressed in terms of the diagonals.

... moreUsing the Pythagorean theorem, for 3 different screen resolutions:

Using the Diagonal Resolution from the previous formula we calculate the PPI for 3 corresponding screen sizes :

**Results:**

**10.1** inch tablet screen of resolution **1024×600** : **117.5PPI****21.5** inch PC monitor of **1080p** resolution : **102.46PPI****27** inch PC monitor of **1440p** resolution : **108.78PPI**

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.

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 Â© 2014 David Lippman and Melonie Rasmussen

http://www.opentextbookstore.com/precalc/

Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

The Vickers hardness test was developed in 1921 by Robert L. Smith and George E. Sandland at Vickers Ltd as an alternative to the Brinell method to measure ... more

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree ... more

Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. The ratio of the long diagonal to the ... 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

Morleyâ€™s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... more

In geometry, Napoleon’s theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, ... more

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PPI can be calculated from knowing the diagonal size of the screen in inches and the resolution in pixels (width and height). This can be done in two steps