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Crossing
Ladders
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Step 3: Ratio of AC and GHWe follow the same procedure as in Step 2 to use the Pythagorean Theorem to derive the ratio between AC and GH. Triangle CGAWe observe triangle CGA:
As described above, according to the Pythagorean Theorem, the square of the hypotenuse equals the square of the base plus the square of the height. In the triangle CGA above:
We know that the value of the line CG is 25, and we can substitute:
and simplify:
By looking at the diagram above, we notice that the line GA is comprised of the line HA plus the line GH, so be can substitute, in place of GA2 , the value (HA + GH)2 as follows:
Notice that the value of line HA is the same as the value of line OB, and we know that line OB equals 5. Thus we can substitute for HA with this value:
Further simplifying:
Simplifying again, we derive the fifth basic equation and complete Step 3:
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