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Question Number 139075 by bramlexs22 last updated on 22/Apr/21

Answered by mr W last updated on 22/Apr/21

$$\tan \alpha =\frac{x}{144}$$$$\tan \beta =\frac{x}{144+81}=\frac{x}{225}$$$$\tan \gamma =\frac{x}{225+99}=\frac{x}{324}$$$$\tan \gamma =\tan (90°-\alpha -\beta )=\frac{1}{\tan (\alpha +\beta )}$$$$\frac{x}{324}=\frac{1-\frac{x}{144}\times \frac{x}{225}}{\frac{x}{144}+\frac{x}{225}}=\frac{3600}{41x}(1-\frac{x^2}{32400})$$$$77x^2=36\times 32400$$$$\Rightarrow x=\frac{1080}{\sqrt{77}}\approx 123.077$$

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