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Question Number 179688 by Acem last updated on 01/Nov/22

Commented by HeferH last updated on 01/Nov/22

Commented by HeferH last updated on 01/Nov/22

$$\varphi =30°$$$$$$

Commented by CElcedricjunior last updated on 01/Nov/22

$$calculons\mathbf{\varnothing }$$$$d^{\prime }\mathit{a}\mathit{p}\mathit{r}\stackrel{`}{\mathit{e}}sletheoremedessinus$$$$\frac{\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}15}=\frac{\mathit{b}}{\mathit{s}\mathit{i}\mathit{n}\left(30\right)}=\frac{\mathit{k}}{\mathit{s}\mathit{i}\mathit{n}135}=>\frac{\mathit{b}}{\mathit{x}}=2\mathit{c}\mathit{o}\mathit{s}15\left(1\right)$$$$\frac{\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}\mathbf{\varnothing }}=\frac{\mathit{b}}{\mathit{s}\mathit{i}\mathit{n}45}=\frac{\mathit{m}}{\mathit{s}\mathit{i}\mathit{n}\mathbf{\Omega }}=>\frac{\mathit{b}}{\mathit{x}}=\frac{\mathit{s}\mathit{i}\mathit{n}45}{\mathit{s}\mathit{i}\mathit{n}\mathbf{\varnothing }}\left(2\right)$$$$\left(1\right)=\left(2\right)$$$$\iff \frac{\mathit{s}\mathit{i}\mathit{n}45}{\mathit{s}\mathit{i}\mathit{n}\mathbf{\varnothing }}=2\mathit{c}\mathit{o}\mathit{s}15$$$$\iff \mathit{s}\mathit{i}\mathit{n}\mathbf{\varnothing }=\frac{\mathit{s}\mathit{i}\mathit{n}45}{2\mathit{c}\mathit{o}\mathit{s}15}=\frac{2}{2\sqrt{2}\left(\sqrt{\sqrt{3}+2}\right)}=\frac{1}{\sqrt{2\sqrt{3}+4}}$$$$\mathit{s}\mathit{i}\mathit{n}\mathbf{\varnothing }=\frac{\sqrt{2\sqrt{3}+4}}{2\sqrt{2}+4}$$$$=>\mathbf{\varnothing }=\mathit{a}\mathit{r}\mathit{s}\mathit{i}\mathit{n}\left(\frac{\sqrt{2\sqrt{3}+4}}{2\sqrt{3}+4}\right)=21.47°$$$$..........lecelebrecedricjunior.............$$

Commented by Acem last updated on 01/Nov/22

$$SirHeferH,thesamewayofmine,thanks$$

Commented by Acem last updated on 01/Nov/22

$$MonsieurJunior,mercibeaucoup,$$$$mais{l}^{\prime }angleest30°$$

Answered by mr W last updated on 01/Nov/22

$$anotherway$$$$$$$$\frac{\sin (45+\varphi )}{\sin \varphi }=\frac{\sin (45-15)}{\sin 15}$$$$(1+\frac{1}{\tan \varphi })\frac{1}{\sqrt{2}}=\frac{1}{2\sin 15}=\frac{2}{\sqrt{6}-\sqrt{2}}$$$$\tan \varphi =\frac{1}{\sqrt{3}}$$$$\Rightarrow \varphi =30°$$

Commented by Acem last updated on 01/Nov/22

$$Good!$$

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