Difference between revisions of "1982 AHSME Problems/Problem 22"
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+ | {{AHSME box|year=1982|num-b=21|num-a=23}} | ||
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+ | [[Category:Intermediate Geometry Problems]] |
Latest revision as of 18:12, 25 December 2020
Problem 22
In a narrow alley of width a ladder of length is placed with its foot at point P between the walls. Resting against one wall at , the distance k above the ground makes a angle with the ground. Resting against the other wall at , a distance h above the ground, the ladder makes a angle with the ground. The width is equal to
Solution
We know that and Therefore, Because the two ladders are the same length, we know that Since is isosceles with vertex angle we can conclude that it must be equilateral. Now, since is a right triangle and we can conclude that Because is equilateral, we know that It then follows that Because of ASA, From there, it follows that Since is the width of the alley, the answer is
~ Saumya Singhal
See also
1982 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |