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Question-86932




Question Number 86932 by jagoll last updated on 01/Apr/20
Answered by mr W last updated on 01/Apr/20
1.  RS=RT  5(x−3)+6=4(2x−6)  15=3x  ⇒x=5    2.  ((sin α)/(60))=((sin 50)/(250))=((sin (α+50))/x)  ⇒sin α=((60 sin 50)/(250))  x=((sin (α+50))/(sin 50))×250  =(((sin α)/(tan 50))+cos α)×250  =284.31
$$\mathrm{1}. \\ $$$${RS}={RT} \\ $$$$\mathrm{5}\left({x}−\mathrm{3}\right)+\mathrm{6}=\mathrm{4}\left(\mathrm{2}{x}−\mathrm{6}\right) \\ $$$$\mathrm{15}=\mathrm{3}{x} \\ $$$$\Rightarrow{x}=\mathrm{5} \\ $$$$ \\ $$$$\mathrm{2}. \\ $$$$\frac{\mathrm{sin}\:\alpha}{\mathrm{60}}=\frac{\mathrm{sin}\:\mathrm{50}}{\mathrm{250}}=\frac{\mathrm{sin}\:\left(\alpha+\mathrm{50}\right)}{{x}} \\ $$$$\Rightarrow\mathrm{sin}\:\alpha=\frac{\mathrm{60}\:\mathrm{sin}\:\mathrm{50}}{\mathrm{250}} \\ $$$${x}=\frac{\mathrm{sin}\:\left(\alpha+\mathrm{50}\right)}{\mathrm{sin}\:\mathrm{50}}×\mathrm{250} \\ $$$$=\left(\frac{\mathrm{sin}\:\alpha}{\mathrm{tan}\:\mathrm{50}}+\mathrm{cos}\:\alpha\right)×\mathrm{250} \\ $$$$=\mathrm{284}.\mathrm{31} \\ $$

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