Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. Trigonometry is used a ton in the modern world. Some examples of real life applications include mapping, measuring the heights of buildings and objects, landscaping, and anything that uses angles and side lengths. It is also used in finding the distances of celestial bodies. Lets look at an example of using trigonometry to find the height of an object.
So lets say you have a building in front of you. You know that the building is 500 ft tall and you are 300 ft away from it. The angle from the point you are standing to the top of the building is37 degrees. We are using a special triangle for simplicity, but pretend you do not know the side lengths or the angles. Since it is a right triangle because the building goes up at a 90 degree angle, we can use SOCATOA. Since we know that a triangles angles should add up to 180, we can use subtraction to find the new angle. 90 + 37 =127. 180-127= 53. Using Pythagorean Theorem, we can find the last side length.
But what if the triangle is not a right triangle? What do we use then? There are number of ways in which we can solve non-right triangles. A few ways include the Law of Sines and Law of Cosines. Lets look at some examples of both:
To solve an SSA triangle
A picture demonstration:
To solve an SSA triangle
- use The Law of Sines first to calculate one of the other two angles;
- then use the three angles add to 180° to find the other angle;
- finally use The Law of Sines again to find the unknown side.
- To solve an SSS triangle:
- use The Law of Cosines first to calculate one of the angles.
- then use The Law of Cosines again to find another angle.
- and finally use angles of a triangle add to 180° to find the last angle.
A picture demonstration:
Once again, these processes can be used in many different areas. Construction, art, mathematics, architecture, and many others including astronomy, surveyors, and pretty much anything using any type of triangle.