Hi guys! I've been doing review for my math and noticed the 60-60-30 triangle in trigonometry. Are these important to know for standardized tests like the ACT or SAT? Thanks in advance.
Hello! In regards to your question about 60-30-90 triangles (I believe that's what you meant, as 60-60-30 would result in a triangle with angles summing to more than 180 degrees), yes, this type of triangle does show up reasonably often on standardized tests such as the SAT or ACT.
Understanding the relationship of the sides in a 60-30-90 triangle can often simplify the computation and help find solutions more quickly. To elaborate, in a 60-30-90 triangle, the shorter leg (opposite the 30-degree angle) is half the length of the hypotenuse and the longer leg (opposite the 60-degree angle) is √3/2 times the hypotenuse.
Towards this end, make sure to master the relationships and how to leverage it when you see right triangles in test problems. Similarly, knowledge of other special triangles such as 45-45-90 triangles can also be helpful in navigating the Math sections of these standardized tests. It helps you compute distances and angles quicker, which can be beneficial given the timed nature of these exams.
For instance, if you encounter a geometry problem involving an equilateral triangle (a triangle with all sides equal), you can split this into two 30-60-90 triangles to help calculate lengths or area.
Remember, in the realm of standardized testing, every second counts and the less time you spend on computation, the more time you can allocate toward solving complex problems. Good luck with your test preparations!
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