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Question Number 209639 by SonGoku last updated on 17/Jul/24

Commented by SonGoku last updated on 17/Jul/24

$$\mathrm{In}\mathrm{the}\mathrm{figure},\mathrm{DC}//\mathrm{FG}\mathrm{is}\mathrm{the}\mathrm{width}\mathrm{of}\mathrm{a}\mathrm{river}.$$$$\mathrm{How}\mathrm{wideis}\mathrm{this}\mathrm{river}?$$$$(\mathrm{How}\mathrm{do}\mathrm{I}\mathrm{solve}\mathrm{it}?)$$

Answered by mr W last updated on 17/Jul/24

Commented by SonGoku last updated on 17/Jul/24

$$\mathrm{You}\mathrm{are}\mathrm{fantastic}!$$$$\mathrm{I}\mathrm{learn}\mathrm{a}\mathrm{lot}\mathrm{from}\mathrm{your}\mathrm{elegantt}\mathrm{soluions}.$$$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}.$$

Commented by SonGoku last updated on 17/Jul/24

$$\mathrm{Did}\mathrm{you}\mathrm{use}\mathrm{the}\mathrm{law}\mathrm{of}\mathrm{sines}?$$$$$$$$\frac{\mathrm{y}}{\sin 17°0^{\prime }{50}^{″}}=\frac{50}{\sin 90°}$$

Commented by mr W last updated on 17/Jul/24

$$y=widthofriver$$$$y=50\sin \alpha$$$$\cos \alpha =\frac{2.9^2+1.3^2-1.7^2}{2\times 2.9\times 1.3}=0.956233$$$$\Rightarrow \sin \alpha =\sqrt{1-0.{956233}^2}=0.292605$$$$\Rightarrow y=50\times 0.292605=14.63m$$

Commented by mr W last updated on 17/Jul/24

$$intherighttriangle:$$$$\frac{y}{50}=\sin \alpha$$$$y=50\times \sin \alpha$$

Commented by mr W last updated on 17/Jul/24

Commented by SonGoku last updated on 17/Jul/24

$$\mathrm{It}\mathrm{is}\mathrm{always}\mathrm{an}\mathrm{honor}\mathrm{to}\mathrm{learn}\mathrm{from}\mathrm{you}.$$$$\mathrm{My}\mathrm{sincereh}\mathrm{tanks}.$$

Commented by mr W last updated on 17/Jul/24

$$thankstoyoutoo!$$

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