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Question Number 206885 by efronzo1 last updated on 29/Apr/24

Answered by BaliramKumar last updated on 29/Apr/24

$$x={\tan }^{-1}\left(\frac{5}{8}\right)\approx 32°$$

Answered by Rasheed.Sindhi last updated on 29/Apr/24

$$\mathrm{Four}\mathrm{triangles}+\mathrm{smaller}\mathrm{square}=\mathrm{large}\mathrm{square}$$$$\frac{a(a+3)}{2}\times 4+9=89\left[aissmallersideofatriangle\right]$$$$2a^2+6a-80=0$$$$a^2+3a-40=0$$$$(a+8)(a-5)=0$$$$a\ne -8\Rightarrow a=5$$$$\tan x=\frac{5}{8}$$$$x={\tan }^{-1}\left(\frac{5}{8}\right)\approx 32°$$

Answered by Rasheed.Sindhi last updated on 29/Apr/24

$$Letsmallersideoftriangleisa$$$$a^2+{(a+3)}^2=89\left[\mathrm{Pythagoras}\mathrm{theorm}\right]$$$$2a^2+6a+9-89=0$$$$a^2+3a+40=0$$$$(a+8)(a-5)=0$$$$a\ne -8\Rightarrow a=5$$$$\tan x=\frac{a}{a+3}=\frac{5}{8}$$$$x={\tan }^{-1}\left(\frac{5}{8}\right)=32°$$

Answered by mr W last updated on 30/Apr/24

$$s^2=89$$$$4\times \frac{1}{2}\times s^2\sin x\cos x=89-9=80$$$$\Rightarrow \sin 2x=\frac{80}{89}$$$$\Rightarrow x=\frac{1}{2}{\sin }^{-1}\frac{80}{89}\approx 32°$$

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