Question-139075

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

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

\tan α = \frac{x}{144}

\tan β = \frac{x}{144 + 81} = \frac{x}{225}

\tan γ = \frac{x}{225 + 99} = \frac{x}{324}

\tan γ = \tan (90 ° - α - β) = \frac{1}{\tan (α + β)}

\frac{x}{324} = \frac{1 - \frac{x}{144} \times \frac{x}{225}}{\frac{x}{144} + \frac{x}{225}} = \frac{3600}{41 x} (1 - \frac{x^{2}}{32400})

77 x^{2} = 36 \times 32400

\Rightarrow x = \frac{1080}{\sqrt{77}} \approx 123.077

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