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A-man-standing-on-top-of-Burj-Khalifa-If-the-height-of-Burj-Khalifa-including-a-man-is-830-m-then-what-is-the-maximum-distance-up-to-which-a-man-can-see-objects-on-Earth-Earth-s-radius-6371-km-




Question Number 196774 by BaliramKumar last updated on 31/Aug/23
  A man standing on top of Burj Khalifa.  If the height of Burj Khalifa including a man is 830 m, then what is the maximum distance up to which a man can see objects on Earth?  (Earth's radius 6371 km)
$$ \\ $$A man standing on top of Burj Khalifa. If the height of Burj Khalifa including a man is 830 m, then what is the maximum distance up to which a man can see objects on Earth? (Earth's radius 6371 km)
Answered by Frix last updated on 31/Aug/23
h=.83km  r=6371km    (h+r)^2 =x^2 +r^2   x=(√(h(h+2r)))≈102.84km
$${h}=.\mathrm{83km} \\ $$$${r}=\mathrm{6371km} \\ $$$$ \\ $$$$\left({h}+{r}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} +{r}^{\mathrm{2}} \\ $$$${x}=\sqrt{{h}\left({h}+\mathrm{2}{r}\right)}\approx\mathrm{102}.\mathrm{84km} \\ $$
Commented by BaliramKumar last updated on 31/Aug/23
Commented by BaliramKumar last updated on 31/Aug/23
Please Sir,  green arc distance solution
$$\mathrm{Please}\:\mathrm{Sir},\:\:\mathrm{green}\:\mathrm{arc}\:\mathrm{distance}\:\mathrm{solution} \\ $$
Commented by mahdipoor last updated on 31/Aug/23
cosα=(r/(h+r)) , arc=rα
$${cos}\alpha=\frac{{r}}{{h}+{r}}\:,\:{arc}={r}\alpha \\ $$
Commented by Frix last updated on 01/Sep/23
Yes.
$$\mathrm{Yes}. \\ $$
Commented by mr W last updated on 01/Sep/23
α=cos^(−1) ((6371)/(6371+0.83))≈0  α≈tan α  arc=rα≈r tan α=x  compare:  arc=ra=102.833 km  x=r tan α=102.842 km
$$\alpha=\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{6371}}{\mathrm{6371}+\mathrm{0}.\mathrm{83}}\approx\mathrm{0} \\ $$$$\alpha\approx\mathrm{tan}\:\alpha \\ $$$${arc}={r}\alpha\approx{r}\:\mathrm{tan}\:\alpha={x} \\ $$$${compare}: \\ $$$${arc}={ra}=\mathrm{102}.\mathrm{833}\:{km} \\ $$$${x}={r}\:\mathrm{tan}\:\alpha=\mathrm{102}.\mathrm{842}\:{km} \\ $$
Commented by BaliramKumar last updated on 01/Sep/23
thanks sir
$$\mathrm{thanks}\:\mathrm{sir} \\ $$

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