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Question Number 208467 by Tawa11 last updated on 16/Jun/24

Answered by A5T last updated on 17/Jun/24

Commented by A5T last updated on 17/Jun/24

$$sin\theta =\frac{3\sqrt{10}}{10}\Rightarrow cos\theta =\frac{\sqrt{10}}{10}$$$$sin(135-\theta )=\frac{1}{\sqrt{2}}(cos\theta +sin\theta )=\frac{\sqrt{20}}{5}\Rightarrow cos(135-\theta )=\frac{\sqrt{5}}{5}$$$$\Rightarrow tan(135-\theta )=2=\frac{3}{x}\Rightarrow x=\frac{3}{2}$$$$\Rightarrow \left[blue\right]=(1+\frac{3}{2})\times 3\times \frac{1}{2}=\frac{15}{4}$$

Commented by Tawa11 last updated on 17/Jun/24

$$\mathrm{Thanks}\mathrm{sir}$$

Answered by efronzo1 last updated on 17/Jun/24

Commented by Tawa11 last updated on 17/Jun/24

$$\mathrm{Thanks}\mathrm{sir}.$$

Answered by mr W last updated on 21/Jun/24

Commented by mr W last updated on 21/Jun/24

$$\sqrt{10}=\frac{1}{\sqrt{10}}x+\frac{3}{\sqrt{10}}x=\frac{4x}{\sqrt{10}}$$$$\Rightarrow x=\frac{5}{2}$$$$A_{blue}=\frac{3}{2}\times \frac{5}{2}=\frac{15}{4}$$

Commented by Tawa11 last updated on 21/Jun/24

$$\mathrm{Thanks}\mathrm{sir}.$$$$\mathrm{Sir}.\sqrt{10}=\frac{\mathrm{x}}{\sqrt{10}}+\frac{3\mathrm{x}}{\sqrt{10}}\mathrm{not}\mathrm{clear}\mathrm{sir}.$$$$\mathrm{Sorry}\mathrm{to}\mathrm{be}\mathrm{asking}\mathrm{too}\mathrm{much}$$$$\mathrm{question}\mathrm{sir}.$$

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