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Question Number 212630 by efronzo1 last updated on 19/Oct/24

Commented by efronzo1 last updated on 19/Oct/24

Answered by mr W last updated on 19/Oct/24

Commented by mr W last updated on 19/Oct/24

$$\tan \alpha =\frac{h-\frac{b}{2}}{\frac{b}{2}}=\frac{2h-b}{b}$$$$\tan 2\alpha =\frac{a-\frac{b}{2}}{h}=\frac{2a-b}{2h}$$$$\frac{2a-b}{2h}=\frac{2\times \frac{2h-b}{b}}{1-{\left(\frac{2h-b}{b}\right)}^2}$$$$\frac{2a-b}{2h}=\frac{2\times \frac{2h-b}{b}}{1-{\left(\frac{2h-b}{b}\right)}^2}$$$$let\lambda =\frac{2h}{b}$$$$\frac{2\left(\frac{a}{b}\right)-1}{\lambda }=\frac{2(\lambda -1)}{1-{(\lambda -1)}^2}$$$$\lambda =\frac{4\left(\frac{a}{b}\right)}{2\left(\frac{a}{b}\right)+1}=\frac{2h}{b}$$$$\Rightarrow h=\frac{2ab}{2a+b}✓$$

Commented by Spillover last updated on 20/Oct/24

$$great$$

Answered by Spillover last updated on 19/Oct/24

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