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Question Number 164709 by Tawa11 last updated on 20/Jan/22

Answered by Tawa11 last updated on 20/Jan/22

$$\mathrm{Am}\mathrm{getting}14.28\mathrm{but}\mathrm{answer}\mathrm{at}\mathrm{the}\mathrm{back}\mathrm{is}12.7\mathrm{please}\mathrm{help}.$$

Commented by mr W last updated on 21/Jan/22

$$howdidyouget14.28?maybeyouare$$$$right.this{isn}^{\prime }thardtoyouithink.$$

Commented by mr W last updated on 21/Jan/22

$${OP}_1=\frac{h}{\tan 40°}$$$${OP}_2=\frac{h}{\tan 35°}$$$$P_1{P}_2=10m$$$${OP}_1^2+P_1{P}_2^2={OP}_2^2$$$${\left(\frac{h}{\tan 40°}\right)}^2+{10}^2={\left(\frac{h}{\tan 35°}\right)}^2$$$$h=\frac{10}{\sqrt{\frac{1}{{\tan }^{2}35°}-\frac{1}{{\tan }^{2}40°}}}\approx 12.71m$$

Commented by Tawa11 last updated on 21/Jan/22

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{Sir},\mathrm{please}\mathrm{is}\mathrm{this}\mathrm{diagram}\mathrm{correct}?$$$$\mathrm{Because}\mathrm{the}\mathrm{angle}\mathrm{in}\mathrm{the}\mathrm{triangle}\mathrm{is}\mathrm{more}\mathrm{than}180.$$$$\mathrm{I}\mathrm{interchange}\mathrm{the}\mathrm{angles}\mathrm{and}\mathrm{got}14.28$$

Commented by mr W last updated on 21/Jan/22

$$thepolestandsontheground!$$$$it{doesn}^{\prime }tlieontheground!$$$$allhappensin3Dworld,notin2D.$$

Commented by mr W last updated on 21/Jan/22

$$you{can}^{\prime }tsolveifyou{don}^{\prime }tthinkin$$$$3D,seediagram.$$

Commented by mr W last updated on 21/Jan/22

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{Ohh}.\mathrm{Wow}.\mathrm{great}.\mathrm{I}\mathrm{just}\mathrm{know}\mathrm{this}\mathrm{now}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{The}\mathrm{diagram}\mathrm{now}\mathrm{strange}\mathrm{to}\mathrm{me}\mathrm{to}\mathrm{find}\mathrm{h}.$$

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{Sir},\mathrm{please}\mathrm{find}\mathrm{h}.$$$$\mathrm{I}\mathrm{still}\mathrm{have}\mathrm{more}\mathrm{questions}\mathrm{on}\mathrm{this}\mathrm{aspect}.\mathrm{I}\mathrm{will}\mathrm{solve}\mathrm{them}\mathrm{all}\mathrm{after}\mathrm{your}$$$$\mathrm{wirkings}.\mathrm{I}\mathrm{just}\mathrm{know}\mathrm{this}\mathrm{now}\mathrm{from}\mathrm{you}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$$$\mathrm{Even}\mathrm{if}\mathrm{it}\mathrm{is}\mathrm{short}\mathrm{workings}\mathrm{to}\mathrm{get}\mathrm{h}.$$$$\mathrm{I}\mathrm{will}\mathrm{do}\mathrm{the}\mathrm{rest}.$$

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{understand}\mathrm{better}\mathrm{now}.$$$$\mathrm{Am}\mathrm{happy}.\mathrm{I}\mathrm{can}\mathrm{solve}\mathrm{the}\mathrm{rest}.$$$$\mathrm{That}3\mathrm{D}\mathrm{you}\mathrm{told}\mathrm{me}\mathrm{open}\mathrm{my}\mathrm{eye}\mathrm{to}\mathrm{drawings}\mathrm{now}.$$$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by mr W last updated on 21/Jan/22

$$ithoughtyouwereevenmuchfurther$$$$thanthebookwithyouranswer$$$$14.28m.$$$$asyoucanseeabove,theanswer12.7$$$$massumedthethestudentobserves$$$$thetopofthepolefromthelevel$$$$oftheground,i.e.hiseyesmust$$$$directlylieontheground.thisis$$$$naturallynotpossible.infacthe$$$$canonlyobservewhenhealsostands.$$$$hiseyeshaveaheightovertheground.$$$$ifthisheightis1.57m,whichis$$$$possibleforastudentwithnormal$$$$bodysize,thentheheightofthepole$$$$isactually1.57+12.71=14.28m.$$$$ithoughtyouhadconsideredthis.thus$$$$i{didn}^{\prime }tsaythatyouranswer14.28m$$$$iswrong.$$

Commented by mr W last updated on 21/Jan/22

Commented by mr W last updated on 21/Jan/22

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{Sir},\mathrm{I}\mathrm{have}\mathrm{used}\mathrm{your}3\mathrm{D}\mathrm{thinking}\mathrm{to}\mathrm{interprete}\mathrm{all}\mathrm{the}\mathrm{complex}$$$$\mathrm{diagrams}\mathrm{in}\mathrm{my}\mathrm{book}.\mathrm{I}\mathrm{got}\mathrm{everything}.\mathrm{Am}\mathrm{happy}.$$$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{Wow}.\mathrm{true}\mathrm{sir}.\mathrm{This}\mathrm{is}\mathrm{what}\mathrm{I}\mathrm{thought}.$$

Commented by Tawa11 last updated on 21/Jan/22

$$\mathrm{I}\mathrm{understand}\mathrm{everything}\mathrm{better}\mathrm{now}\mathrm{sir}.$$$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{more}.\mathrm{I}\mathrm{really}\mathrm{appreciate}\mathrm{your}\mathrm{time}.$$

Commented by mr W last updated on 22/Jan/22

$$Q1.whatistheanswerifthestudent$$$$moves10mnotduesouth,but$$$$duewest?$$

Commented by mr W last updated on 22/Jan/22

$$Q2.whatistheanswerifthestudent$$$$moves10mnotduesouth,but$$$$duesouth-west?$$

Commented by Tawa11 last updated on 22/Jan/22

Commented by Tawa11 last updated on 22/Jan/22

$$\tan 40=\frac{\mathrm{h}}{\mathrm{x}},$$$$\therefore \mathrm{x}=\frac{\mathrm{h}}{\tan 40}$$$$\tan 35=\frac{\mathrm{h}}{10+\mathrm{x}}$$$$10+\mathrm{x}=\frac{\mathrm{h}}{\tan 35}$$$$\therefore \mathrm{x}=\frac{\mathrm{h}}{\tan 35}-10$$$$\therefore \frac{\mathrm{h}}{\tan 40}=\frac{\mathrm{h}}{\tan 35}-10$$$$\therefore \mathrm{h}\tan 35=\mathrm{h}\tan 40-10\tan 40\tan 35$$$$\therefore \mathrm{h}(\tan 40-\tan 35)=\frac{10\tan 40\tan 35}{1}$$$$\therefore \mathrm{h}=\frac{10\tan 40\tan 35}{\tan 40-\tan 35}=42.30\mathrm{m}$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Please}\mathrm{check}\mathrm{sir}.$$

Commented by mr W last updated on 22/Jan/22

$$h\approx 42.30m$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Wow},\mathrm{am}\mathrm{correct}\mathrm{sir}.\mathrm{I}\mathrm{have}\mathrm{changed}\mathrm{it}.\mathrm{I}\mathrm{did}\mathrm{not}\mathrm{press}$$$$\mathrm{calculator}\mathrm{directly}\mathrm{before}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Sir},\mathrm{also}\mathrm{in}\mathrm{Bearing}\mathrm{and}\mathrm{Distance}.\mathrm{I}\mathrm{should}\mathrm{be}\mathrm{working}\mathrm{in}3\mathrm{D}\mathrm{too}???$$$$\mathrm{Becsuse}\mathrm{I}\mathrm{will}\mathrm{start}\mathrm{soon}.$$

Commented by mr W last updated on 22/Jan/22

$$whataboutQ2fromabove?$$

Commented by Tawa11 last updated on 22/Jan/22

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Sir},\mathrm{please}\mathrm{check}\mathrm{my}\mathrm{diagram}\mathrm{first}.\mathrm{Hahahaha}.$$

Commented by mr W last updated on 22/Jan/22

$$maybecorrect.yourdiagramisnot$$$$clear.youonlyneedtodrawaground$$$$view.$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Alright}\mathrm{sir}.\mathrm{Let}\mathrm{me}\mathrm{draw}\mathrm{it}.$$

Commented by Tawa11 last updated on 22/Jan/22

Commented by mr W last updated on 22/Jan/22

$$youseemnottorealisewhatis$$$$meantwith‘‘hemoves10mdue$$$$south-{west}^{″}.$$

Commented by Tawa11 last updated on 22/Jan/22

$$\tan 40=\frac{\mathrm{h}}{\mathrm{x}}$$$$\therefore \mathrm{x}=\frac{\mathrm{h}}{\tan 40}$$

Commented by mr W last updated on 22/Jan/22

$$wrong!$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Ok}\mathrm{sir}.\mathrm{I}\mathrm{will}\mathrm{try}\mathrm{again}$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{The}\mathrm{trigonometry}\mathrm{is}\mathrm{hard}\mathrm{for}\mathrm{me}\mathrm{sir}.$$$$\mathrm{But}\mathrm{is}\mathrm{my}\mathrm{diagram}\mathrm{correct}\mathrm{first}?$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Sir},\mathrm{in}\mathrm{your}\mathrm{own}\mathrm{diagram}.\mathrm{How}\mathrm{is}{\mathrm{TOP}}_2=90$$

Commented by mr W last updated on 22/Jan/22

$$whenthepolestandsontheground,$$$$thatmeansitstandsvertically,i.e.$$$$witha90°angletothehorozontal.$$$$\mathrm{\angle }{TOP}_1=90°,\mathrm{\angle }{TOP}_2=90°,....$$$$theseareverybasicthings,ithink.$$

Commented by Tawa11 last updated on 22/Jan/22

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Ohhh}.\mathrm{I}\mathrm{just}\mathrm{see}\mathrm{it}\mathrm{now}\mathrm{sir}.\mathrm{God}\mathrm{bless}\mathrm{you}.$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{Is}\mathrm{my}\mathrm{last}\mathrm{diagram}\mathrm{interprete}\mathrm{what}\mathrm{you}\mathrm{mean}\mathrm{by}10\mathrm{m}\mathrm{due}-\mathrm{south}\mathrm{west}$$$$\mathrm{sir}?$$

Commented by mr W last updated on 22/Jan/22

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{I}\mathrm{see}\mathrm{sir}.\mathrm{It}\mathrm{look}\mathrm{like}\mathrm{my}\mathrm{first}\mathrm{diagram}$$

Commented by mr W last updated on 22/Jan/22

$${what}^{\prime }stheresultforhinQ2?$$

Commented by Tawa11 last updated on 22/Jan/22

$$\mathrm{C}\mathrm{to}\mathrm{the}\mathrm{foot}\mathrm{of}\mathrm{the}\mathrm{pole}$$$$\frac{\sin 10}{10}=\frac{\sin 135}{\mathrm{y}}$$$$\therefore \mathrm{y}=\frac{10\sin 135}{\sin 10}=40.52$$$$\therefore \tan 35=\frac{\mathrm{h}}{40.52}$$$$\therefore \mathrm{h}=40.52\tan 35$$$$\therefore \mathrm{h}=28.37\mathrm{m}$$$$$$$$\mathrm{This}\mathrm{will}\mathrm{be}\mathrm{wrong}\mathrm{because}\mathrm{I}\mathrm{did}\mathrm{not}\mathrm{use}40\mathrm{degrees}\mathrm{in}\mathrm{the}\mathrm{question}.$$$$$$

Commented by mr W last updated on 23/Jan/22

$$i{can}^{\prime }thelpyoutothinkandto$$$$understandin3Dspace.$$$$oneneedssomeabilityforspatia$$$$immaginationforsuchquestions.$$$$$$$${(\frac{h}{\tan 40°}+10\cos 45°)}^2+{\left(10\sin 45°\right)}^2={\left(\frac{h}{\tan 35°}\right)}^2$$$$h\approx 32.2239m$$

Commented by Tawa11 last updated on 23/Jan/22

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{I}\mathrm{really}\mathrm{appreciate}.$$$$\mathrm{I}\mathrm{will}\mathrm{study}\mathrm{more}\mathrm{on}3\mathrm{D}\mathrm{space}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by ajfour last updated on 23/Jan/22

$$goodpursualatleast...$$

Commented by Tawa11 last updated on 23/Jan/22

$$\mathrm{Thanks}\mathrm{sir}.\mathrm{I}\mathrm{learnt}\mathrm{new}\mathrm{thing}.$$

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