Question

I need some help with this problem.

Answer 1

So we are dealing with a 30-60-90 triangle obviously. This is one of those triangles that always has the same ratio of their sides which means if you know one side length of a 30-60-90 you know all the sides.


I have attached a diagram of a 30-60-90 triangle below, we can use it to find the different sides
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1. 2x =AB and x = BC, we know AB=14, since AB is two times as big as BC we know that BC = 7


2. Knowing BC equals 7 we can also say that x=7, since the diagram shows us AC = x times the square root of three we know that AC = 7 times the square root of 3.


3. If AB =16, 16 = 2x, and x=8, plug this into x times the square root of three to get AC, which equals 8 times the square root of three.


4. If AC equals 9 times the square root of three, we know that x=9. Side BC is simply x so BC = 9