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Question-227924




Question Number 227924 by infinityaction last updated on 02/Mar/26
Answered by mr W last updated on 02/Mar/26
A_(intersection) ≥16×((0.5×0.5 tan 22.5°)/2)                        =2((√2)−1)>0.8>(3/4)
$${A}_{{intersection}} \geqslant\mathrm{16}×\frac{\mathrm{0}.\mathrm{5}×\mathrm{0}.\mathrm{5}\:\mathrm{tan}\:\mathrm{22}.\mathrm{5}°}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)>\mathrm{0}.\mathrm{8}>\frac{\mathrm{3}}{\mathrm{4}} \\ $$
Commented by infinityaction last updated on 02/Mar/26
can u explain littlt bit
$${can}\:{u}\:{explain}\:{littlt}\:{bit} \\ $$$$ \\ $$
Commented by mr W last updated on 03/Mar/26
Commented by mr W last updated on 03/Mar/26
due to symmetry the smallest  intersection area is 16 times   the hatched triangle.
$${due}\:{to}\:{symmetry}\:{the}\:{smallest} \\ $$$${intersection}\:{area}\:{is}\:\mathrm{16}\:{times}\: \\ $$$${the}\:{hatched}\:{triangle}. \\ $$

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