Science Library - free educational site

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: $B = tan^{-1}({b/a})$.

Content © Andrew Bone. All rights reserved. Created : February 19, 2014

Latest Item on Science Library:

The most recent article is:

Air Resistance and Terminal Velocity

View this item in the topic:

Mechanics

and many more articles in the subject:

Subject of the Week

Environment

Environmental Science is the most important of all sciences. As the world enters a phase of climate change, unprecedented biodiversity loss, pollution and human population growth, the management of our environment is vital for our futures. Learn about Environmental Science on ScienceLibrary.info.

Environmental Science

Great Scientists

Antonie Philips van Leeuwenhoek

1632 - 1723

Antonie van Leeuwenhoek was a Dutch draper who needed a better way to examine the tiny threads of cloth. His ingenious solution gave birth to the modern science of microbiology!

Anton van Leeuwenhoek
Umwelt.Science

Quote of the day...

When I said I wanted to be a comedian, they laughed. Well, they're not laughing now...

ZumGuy Internet Promotions

Umwelt.Science