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Finding a missing side in a 30 60 90 special right triangle

Website: A Quick Guide to the 30-60-90 TriangleLinks to an external site.

Reference:

By: Mary Jane Sterling and Updated: 08-08-2022 From The Book:  Pre-Calculus For Dummies, By: Mary Jane Sterling and, and, M. J. S.,  08-08-2022, U., From The Book: Pre-Calculus For Dummies, About the book  author: Mary Jane Sterling aught algebra, author:, A. the book, &  algebra, M. J. S. aught. (n.d.). A quick guide to the 30-60-90 triangle. dummies. Retrieved October 5, 2022, from https://www.dummies.com/article/academics-the-arts/math/pre-calculus/quick-guide-to-the-30-60-90-degree-triangle-168056/Links to an external site.

The website linked above gives robust instructions and examples of  how to solve for a missing side on a 30-60-90 special right triangle. It  explains the ratio of the side lengths and how these ratios can be used  to quickly find the lengths. Below is an example of such a triangle:

Assume this example of a 30-60-90 Triangle, we have a triangle with  the known short side of 5 m, and a hypotenuse of 10 m. In this example,  it is easy to find the missing side’s length. By taking the length of  the short side and multiplying it by the square root of 3.

a = 5 m

2a = 10 m

a√3 = ?

(5) √3 = 8.66 m

The answer to this problem is that the missing side equals 8.66 m.