# Trig-Ruler

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Read tigonometry values of SIN and COS directly from scale.

The right triangle has a special place in mathematics because of its interesting characteristics.
In a right triangle, the square of the length of the hypotenuse
is equal to the sum of the squares of its sides. This leads to some special ratios
like sine and cosine, which are used extensively in such fields as science, engineering,
and architecture.

SIN: In a right triangle, the ratio of the length of the Opposite side to its hypotenuse
COS: In a right triangle, the ratio of the length of the Base side to its hypotenuse

(for a given angle θ or theta) is a constant and is called sinθ or the sine of the angle θ.
Its inverse trig function is cosecant, denoted cscθ.

sinθ=Opposite/Hypotenuse
cscθ=1/sinθ=Hypotenuse/Opposite

Ex: The sine of an angle in a right triangle can also
be a measure of steepness.

You can calculate the height of an object (such as a building or a tree) and its distance from you with the help of the Trig Ruler by simply measuring the angle of your line of sight.

To find out how far away an object is, stand at a distance and align the Trig Ruler such that the base is horizontal and parallel to the ground and the hypotenuse is aligned toward the bottom of the object, as shown in Fig 1.2.6. By doing this, you are creating two similar triangles. Using the fact that the sides of similar triangles are proportional, you can find the object’s distance x from you.

Note: You are looking at the object from your height, so the height h is same as your height. The height h' is the reading from the Trig Ruler’s Perpendicular scale and the distance x’ is the reading from the Trig Ruler’s Base scale (where the Base and the Perpendicular intersect). x is the distance from the object to you.

This gives you your distance from the object, x, as: Fig 2.5. Using the Trig Ruler to measure distances

x/h=x'/h'

The height H of the object can be calculated by aligning the hypotenuse toward the top of the object and measuring the Trig Ruler’s Base and Perpendicular scales at the point where they intersect. If the base scale measures x and the perpendicular scale measures h, then the height of the object can be found by using:

H/h=X/x

Fig 2.6. Using the Trig Ruler to find the height of an object

# Coordinate System Board Game

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Learn the basics of Complex Number, Pythagorus Theorem and Vector Arithmatic.

A board game palyed with two 20 face dice, black and white.
Roll the two dice, move your piece in X direction corresponding to the Black dice,
(for negative number move to the left of origin and for positive number move to the right).
Move in Y direction corresponding to the White dice for negative number move down, for positive
number move up. Compute the magnitude of your final location from the origin using the Pythagorean Theorem. Keep track of each person’s magnitudes separately. Add the magnitudes of each successive throw. The person with the highest score after 10 throws wins the game.