The folded length of the ladder is 1.11m, and the distance between its bases when

| August 2, 2021 | education

The folded length of the ladder is 1.11m, and the distance between its bases when unfolded is 72m. find the height of the ladder when unfolded

The unfolded stepladder is an isosceles triangle, its folded length is the length of the side, and the distance between the bases when unfolded is the base of the triangle, the unfolded stepladder height is the height of the isosceles triangle drawn to the base.
Let the step-ladder be △ ABC: AB = BC = 1.11 m, AC = 0.72 m, BH – height.
Since △ ABC is isosceles, BH is both the height and the median: AH = CH = AC / 2 = 0.72 / 2 = 0.36 (m).
Consider △ AHB: ∠AHB = 90 ° (since BH is the height), AB = 1.11 m is the hypotenuse (since it lies opposite the right angle), AH = 0.36 m and BH are the legs.
By the Pythagorean theorem:
BH = √ (AB² – AH²) = √ (1.11² – 0.36²) = √ (1.2321 – 0.1296) = √1.1025 = 1.05 (m).
Answer: BH = 1.05 m.



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