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## Homework Statement

My knowns are: the trapezoid has a perimeter equal to 180 inches

and it's base angles are ∏/3

The unknowns are: the lengths of the base (x) and the length of one of the slanted sides (y)

as well as the relationship between x and y

## Homework Equations

Trig equations

## The Attempt at a Solution

I pretty much split up the trapezoid into 2 right triangles and a rectangle. The triangle creates a 30-60-90 right triangle giving me the length ratios of the sides. This is where I hit my dead end because I have no idea how to find the lengths of the triangles without a single length of any of the triangle's sides. My friend was able to guess and check the correct lengths of x=75 inches and y=30 inches.

I want to know if it's possible to find any of the unknown sides without having to resort to a guess and check method. Also I'm not sure, when it says to deduce a relationship between x and y if it means to create some sort of formula that relates them or something.

Any insight on this is appreciated and thanks in advance.