Right Angle Trigonometry
Motivation
The Pythagorus theorem can be used to calculate the length of the sides of a right angle triangle, which is very useful. The other important feature of a right angle triangle is the angles. Trigonometry links the sides of a right angle triangle with the angles and can be used to calculate the size of any angle provided that at least the length of at least two sides are known. In addition if one angle and one side is known then trigonetry can be used to calculate the length of the other sides. The first step in using trigonetry is to understand the definition of the trigonometric ratios.
The Trig Ratios
The sides must be labelled with respect to the chosen angle.
h=hypotenuse (The longest side of the triangle). op=opposite to the angle. aj=adjacent to the angle.
Press the button to change the selected angle. The hypotenuse remains the same since it is allways the longest side. The opposite and adjacent swap positions.
Cosine abbreviated to cos is the ratio of the adjacent and hypotenuse. Sine abbreviated to sin is the ratio of the opposite and hypotenuse. Tangent abbreviated to tan is the ratio of the opposite and adjacent.Examples of Trig ratios
The triangles are not drawn to scale.
Test your knowledge: write down the ratios before you press the blue button.
The length of the hypotenuse has been rounded to one decimal place. Sometime the ratios can be simplified, and you are recommended to simplify these fractions when appropriate.
Discussion
Familiarity of the trig ratios is the first step in using the trigonometrical functions. A standard scientific calculator has buttons for sin, cos, and tan. The use of these calculators buttons will be discussed in later pages.