Answer:
Step-by-step explanation:
For problems like these, it is helpful to remember the ratios of the side lengths in these special triangles.
45°-45°-90° triangle: 1 : 1 : √2
30°-60°-90° triangle: 1 : √3 : 2
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This means ...
z : 18 : horizontal line = 1 : √3 : 2
z = 18/√3 = 6√3
horizontal line = 2(6√3) = 12√3
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And ...
x : y : horizontal line = 1 : 1 : √2
x = y = (horizontal line)/√2 = (12√3)/√2 = 6√6
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Additional comment
The lengths are easily found as values with a square root in the denominator. Generally, we want the denominator to be a rational number, so we make use of the fact ...
1/√n = (√n)/n
