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Angles

Angle Rules

Right-angle rule

Angle Rules
Straight line angles sum to 180°.

The angles that sub-divide a right angle sum to 90°.

A circle consists of 4 right angles, or 360°. On a graph of a circle, the radial angle enclosed by a right angle is called a quadrant, where quadrant 1 is from 0° to 90°.

Mathematics question
Straight lines form pairs of equal and opposite angles
Mathematics question
An intersecting straight line through parallel lines will form pairs of equal angles

Straight-angle rule

A straight angle is the angle of a straight line, which is 180°. The angles that sub-divide a straight line sum to 180°.

When two straight lines intersect, they form two pairs of angles. The pairs are opposite in position and equal in magnitude.

Pythagoras' Theorem

A famous theorem for calculating the lengths of the sides of a right-angled triangle was invented 2500 years ago by a Greek called Pythagoras. His theorem states:

a2 + b2 = c2, where a and b are the shorter sides of a right-angled triangle with hypotenuse c.

Pythagoras

The Pythagoras or Pythagorean Theorem was devised by the Ancient Greek mathematician, Pythagoras (570 - 495 BCE).

For such a famous man, we actually know relatively little about him for sure. However, his legacy as a mathematician and philosopher has had a huge impact on Western culture in many fields. It is a pity most people today just know him for his eponymous triangle theorem, important as it is.

Pythagoras
Pythagoras in Raphael's School of Athens

Trigonometry

Angles of right-angled triangles may be calculated using trigonometric functions. The definitions of the three basic trig functions are:

Sine

Basic trig identities

The sine of an angle is equal to the length of the opposite side over the hypotenuse: $sinB = b/c$

If two sides of a triangle are known, it is possible to calculate the angle by in the inverse sine function: $B = sin^{-1}({b/c})$.

Cosine

The cosine of an angle is equal to the length of the adjacent side over the hypotenuse: $cosB = a/c$

If two sides of a triangle are known, it is possible to calculate the angle by in the inverse cosine function: $B = cos^{-1}({a/c})$.

Tangent

The tangent of an angle is equal to the length of the opposite side over the adjacent side: $tanB = b/a$

If two sides of a triangle are known, it is possible to calculate the angle by in the inverse tangent function: $B = tan^{-1}({b/a})$.

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Great Scientists

Stephen Hawking

b. 1942

Stephen Hawing is possibly the most-recognisable living scientist. His work in cosmology is considered the most advanced in explaining phenomena such as black holes, and unites general relativity with quantum mechanics.

Stephen Hawking, b. 1942, English physicist
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Des violons
De l'automne
Blessent mon coeur
D'une langeur
Monotone

(The long sobbings of autumn violins
wound my heart with a monotonous languor)

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