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Question Number 217949 by hardmath last updated on 23/Mar/25

Commented by hardmath last updated on 23/Mar/25

$${\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2=?$$

Answered by A5T last updated on 23/Mar/25

$$\frac{\sin 90°}{\mathrm{x}}=\frac{\sin 70°}{1}\Rightarrow \mathrm{x}=\frac{1}{\sin 70°}$$$$\mathrm{Similarly},\mathrm{we}\mathrm{get}\mathrm{y}=\frac{1}{\sin 50°};\mathrm{z}=\frac{1}{\sin 10°}$$$$\Rightarrow {\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2=\frac{1}{{\sin }^{2}50°}+\frac{1}{{\sin }^{2}10°}+\frac{1}{{\sin }^{2}70}=36$$

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