Answer:
6 ft
Explanation:
You want the length of the short side of a 30°-60°-90° triangle, given the longest side is 12 ft.
Special triangle
A 30°-60°-90° triangle has side lengths in the ratios ...
1 : √3 : 2
Here, the longest side is given as 12 ft, so we can multiply this set of ratios by 6 ft to find the lengths of all of the sides:
1 : √3 : 2 = (6 ft) : (6√3 ft) : (12 ft)
The shortest side has length ...
k = 6 ft
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Additional comment
You can also use trig functions to find the length k:
k/(12 ft) = cos(60°) = 1/2, or
k/(12 ft) = sin(30°) = 1/2
k = (1/2)(12 ft) = 6 ft