Smartphones and game consoles have accelerometers and gyroscopes that function using principles of trigonometry. When you play motion-sensing games or use fitness tracking apps, trigonometry is working behind the scenes. 

Two triangles are similar when they have the same shape. That means their corresponding angles are equal and that the length of corresponding sides are scaled by a common scale factor.

The factor a similar figure has been scaled up or down by. The scale factor is a number larger than 1 in the case of a scale-up, and a number between 0 and 1 in the case of a scale-down.

A ratio is a relationship between two numbers indicating how many times the first number contains the second. It is a way to compare quantities of the same kind by division. Ratios can be expressed in various forms, such as "a to b", "a:b", or as a fraction 

Given an acute angle in a right triangle, the adjacent leg is a part of the angle

Given an acute angle in a right triangle, the opposite leg is across from the angle

The longest side in a right triangle and the side across from the right angle

Mathagon

Definition

Adjacent and Opposite Legs

Ratios of the Sides of Similar Right Triangles

Introduction to Trigonometry

Trigonometry is the study of the relationships between the angles and sides of triangles. Watch this video for a quick summary of the basic ideas. 

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What Is Trigonometry?

The edges in a right triangle are known as the adjacent leg, opposite leg, and hypotenuse. This video explains how they’re determined relative to an angle. 

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What Are the Adjacent and Opposite Legs of an Angle?

For any two similar right triangles, the corresponding side ratios are equal. This is an important tenet of trigonometry, and it’s explained more in this video. 

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