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Question Number 217199 by cherokeesay last updated on 05/Mar/25

Commented by cherokeesay last updated on 05/Mar/25

$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}$$

Answered by mr W last updated on 06/Mar/25

$$x=\sqrt{1^2+2^2-1\times 2}=\sqrt{3}$$$$generallyx=\sqrt{a^2+b^2-ab}$$

Commented by mr W last updated on 05/Mar/25

Commented by cherokeesay last updated on 05/Mar/25

$$thankyousomuch$$$$master!$$

Answered by profcedricjunior last updated on 05/Mar/25

$$$$$${\mathit{d}}^{\prime }\mathit{a}\mathit{p}\mathit{r}\mathit{e}\mathit{s}\mathit{l}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{o}\mathit{r}\mathit{e}\mathit{m}\mathit{e}\mathit{d}\mathit{e}\mathit{s}\mathit{s}\mathit{i}\mathit{n}\mathit{u}\mathit{s}$$$$\frac{\mathit{c}}{\mathit{s}\mathit{i}\mathit{n}30}=\frac{3+\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}\left(120\right)}=2\mathit{r}=\frac{{\mathit{c}}^2(\mathit{x}+3)}{2\mathit{A}}\left(1\right)$$$$\frac{1}{\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\alpha }\right)}=\frac{\mathit{c}}{\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }}=\frac{\mathit{b}}{\mathit{s}\mathit{i}\mathit{n}30}\left(2\right)$$$$\frac{2}{\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\beta }\right)}=\frac{\mathit{c}}{\mathit{s}\mathit{i}\mathit{n}\mathit{\sigma }}=\frac{\mathit{d}}{\mathit{s}\mathit{i}\mathit{n}30}\left(3\right)\mathit{o}\mathit{r}\mathit{\beta }=2\mathit{\alpha }\mathit{e}\mathit{t}\mathit{\alpha }+\mathit{\beta }=60$$$$\frac{\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}60}=\frac{\mathit{d}}{\mathit{s}\mathit{i}\mathit{n}(180-\mathit{\theta })}=\frac{\mathit{b}}{\mathit{s}\mathit{i}\mathit{n}(180-\mathit{\sigma })}=\frac{\mathit{d}}{\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }}=\frac{b}{\mathit{s}\mathit{i}\mathit{n}\mathit{\sigma }}\left(4\right)$$$$\left(3\right)=>\mathit{c}=\frac{2\mathit{s}\mathit{i}\mathit{n}\mathit{\sigma }}{\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\beta }\right)}\mathit{d}\mathit{a}\mathit{n}\mathit{s}\left(2\right)=>\frac{1}{\mathit{s}\mathit{i}\mathit{n}\mathit{\alpha }}=\frac{2\mathit{s}\mathit{i}\mathit{n}\mathit{\sigma }}{\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\theta }\right)\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\beta }\right)}=\frac{\mathit{b}}{\mathit{s}\mathit{i}\mathit{n}30}$$$$=>\mathit{b}=\frac{2\mathit{s}\mathit{i}\mathit{n}30\times \mathit{s}\mathit{i}\mathit{n}\mathit{\sigma }}{\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\theta }\right)\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\beta }\right)}\mathit{d}\mathit{a}\mathit{n}\mathit{s}\left(4\right)$$$$\frac{\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}60}=\frac{2\mathit{s}\mathit{i}\mathit{n}\left(30\right)}{s\mathit{i}\mathit{n}\left(\mathit{\theta }\right)\mathit{s}\mathit{i}\mathit{n}\left(\mathit{\beta }\right)}$$$$\mathit{o}\mathit{r}\mathit{\beta }=40;\mathit{\theta }=140$$$$=>\mathit{x}=\frac{2\mathit{s}\mathit{i}\mathit{n}\left(30\right)}{\mathit{s}\mathit{i}\mathit{n}\left(140\right)\times \mathit{s}\mathit{i}\mathit{n}\left(40\right)}$$$$$$

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