Menu Close

Category: Geometry

Question-181619

Question Number 181619 by mr W last updated on 27/Nov/22 Commented by mr W last updated on 27/Nov/22 $${a}\:{goat}\:{is}\:{connected}\:{through}\:{a}\:{ring}\:{with} \\ $$$${a}\:{rope}\:{of}\:\mathrm{30}\:{m}\:{length}\:{whose}\:{ends}\:{are} \\ $$$${fixed}\:{at}\:{two}\:{points}\:{with}\:{a}\:{distance}\:{of} \\ $$$$\mathrm{20}\:{m}\:{as}\:{shown}.\:{a}\:{gate}\:{at}\:{point}\:{C}\:{on}…

Question-181581

Question Number 181581 by HeferH last updated on 27/Nov/22 Answered by a.lgnaoui last updated on 27/Nov/22 $$\bigtriangleup\mathrm{ACD}\:\:\:\measuredangle\mathrm{ADC}=\mathrm{162}\:\:\:\mathrm{sin}\:\left(\mathrm{162}\right)=\mathrm{sin}\:\mathrm{18} \\ $$$$\frac{\mathrm{AC}}{\mathrm{sin}\:\mathrm{18}}=\frac{\mathrm{CD}}{\mathrm{sin}\:\mathrm{12}}\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\measuredangle\mathrm{BDC}=\mathrm{18}\:\:\measuredangle\mathrm{DCB}=\mathrm{162}−\alpha \\ $$$$\frac{\mathrm{BD}}{\mathrm{sin}\:\left(\mathrm{162}−\alpha\right)}=\frac{\mathrm{CD}}{\mathrm{sin}\:\alpha}\:\left(\mathrm{BD}=\mathrm{AC}\right)\Rightarrow \\ $$$$\frac{\mathrm{AC}}{\mathrm{sin}\:\left(\mathrm{162}−\alpha\right)}=\frac{\mathrm{CD}}{\mathrm{sin}\:\alpha}\:\:\left(\mathrm{2}\right)…

Question-181437

Question Number 181437 by mnjuly1970 last updated on 25/Nov/22 Answered by MJS_new last updated on 25/Nov/22 $$\mathrm{let}\:{d},\:\sqrt{{b}^{\mathrm{2}} +{d}^{\mathrm{2}} }\:\mathrm{the}\:\mathrm{other}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangular} \\ $$$$\mathrm{triangle} \\ $$$${p}+{q}=\sqrt{{b}^{\mathrm{2}} +{d}^{\mathrm{2}} };\:{h}^{\mathrm{2}}…