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Question Number 129674 by help last updated on 17/Jan/21

Commented by help last updated on 17/Jan/21

$$10b?$$

Answered by bemath last updated on 18/Jan/21

$$\mathrm{let}\alpha =\mathrm{\angle }(\mathrm{VAB},\mathrm{ABPQ})$$$$\mathrm{let}\mathrm{x}=\mathrm{\angle }(\mathrm{VAB},\mathrm{ABCD})$$$$\mathrm{let}\theta =\mathrm{\angle }(\mathrm{ABPQ},\mathrm{ABCD})$$$$\alpha =\mathrm{x}-\theta$$$$\tan \alpha =\frac{\tan \mathrm{x}-\tan \theta }{1+\tan \mathrm{x}\tan \theta }=\frac{4-\frac{4}{3}}{1+4.\frac{4}{3}}=\frac{8}{19}$$$$\alpha ={\tan }^{-1}\left(\frac{8}{19}\right)=0.398522\mathrm{rad}$$$${\tan }^{-1}\left(\frac{8}{19}\right)$$$$0.398522$$$$$$

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