In week 16 of Precalc 11, I learned how to find the exact trigonometric ratios of special triangles without using technology. I chose to write about this topic because Trigonometry is a heavily calculator-based unit in Pre-Calculus, and it is best not to rely on the calculator for everything.
Before finding the ratios, you must first know what special triangles are. Imagine you have a right triangle, which means it has one angle that is exactly 90 degrees, like a square corner. Now, in special triangles, we focus on two kinds: the 45-45-90 triangle and the 30-60-90 triangle.
- 45-45-90 triangle:
- 30-60-90 triangle:
To find ratios, you must find the x and y of the triangle by putting it on a graph, using SOH CAH TOA, and using the CAST rule (figuring out whether the ratio is positive).
Examples:
