Trigonometry: Angles with sine, cosine and tangent
Rules for right-angled triangles
There is an important rule for right-angled triangles pertaining the ratio between the sides.
When it comes to the lengths of the sides of a right-angled triangle with a right angle , legs and and hypotenuse (the longest side of a right-angled triangle) , the following rule applies:
We call this rule the Pythagorean theorem.
With this theorem, we can calculate the remaining side of a right-angled triangle of which we already know two sides.
For example, if we want to calculate the hypotenuse, we isolate in the Pythagorean theorem:
In a right-angled triangle with right angle is the and are and the legs of the triangle:
- is the of
- is the of
In addition to the ratio between the sides of a right-angled triangle, there are important relationships between the sides and angles of a right-angled triangle.
In a right-angled triangle with right angle we define:
We call (sine), (cosine) and (tangent) trigonometric functions.
With these trigonometric functions we can calculate, using an angle and a side, the remaining sides in a right-angled triangle. We can also calculate the angle using two sides and the inverse.
Keep in mind that you are not allowed to use scientific calculator with , and functions in OMPT exams. These exercises are just there to make the subject matter more concrete and to show that it is possible to calculate , and using a calculator. However, it is not needed in OMPT exams because all the question can be answered exact. Furthermore, in the OMPT exams we use numbers you can calculate by heart.
Or visit omptest.org if jou are taking an OMPT exam.