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Category: Geometry

A-vertical-post-of-height-h-m-rises-from-a-plane-which-slopes-down-towards-the-South-at-an-angle-to-the-horizontal-Prove-that-the-length-of-its-shadow-when-the-sun-is-S-W-at-an-elevation-is-

Question Number 115642 by 24224 Opiyo Kamuki last updated on 27/Sep/20 $${A}\:{vertical}\:{post}\:{of}\:{height}\:{h}\:{m}\:{rises}\:{from}\:{a}\:{plane}\:{which}\: \\ $$$${slopes}\:{down}\:{towards}\:{the}\:{South}\:{at}\:{an}\:{angle} \\ $$$$\alpha\:{to}\:{the}\:{horizontal}.\:{Prove}\:{that}\:{the}\:{length} \\ $$$${of}\:{its}\:{shadow}\:{when}\:{the}\:{sun}\:{is}\:\boldsymbol{{S}\theta{W}}\:\: \\ $$$${at}\:{an}\:{elevation}\:\beta\:{is} \\ $$$$ \\ $$$$\frac{{h}\sqrt{\left(\mathrm{1}+{tan}^{\mathrm{2}} \alpha\:{cos}^{\mathrm{2}}…

Let-the-acute-triangle-ABC-have-an-outer-circumscribed-circle-whose-tangents-at-the-points-B-and-C-intersect-at-point-P-Let-D-and-E-be-the-projections-of-perpendicular-lines-from-point-P-on-AC-and

Question Number 181125 by depressiveshrek last updated on 21/Nov/22 $${Let}\:{the}\:{acute}\:{triangle}\:\Delta{ABC}\:\:{have} \\ $$$${an}\:{outer}\:{circumscribed}\:{circle}, \\ $$$${whose}\:{tangents}\:{at}\:{the}\:{points}\:{B}\:{and}\:{C} \\ $$$${intersect}\:{at}\:{point}\:{P}.\:{Let}\:{D}\:{and}\:{E}\:{be} \\ $$$${the}\:{projections}\:{of}\:{perpendicular} \\ $$$${lines}\:{from}\:{point}\:{P}\:{on}\:{AC}\:{and}\:{AB}. \\ $$$${Prove}\:{that}\:{the}\:{interdection}\:{point}\:{of} \\ $$$${the}\:{heights}\:{of}\:\Delta{ADE}\:{is}\:{the}\:{midpoint} \\…

Question-49984

Question Number 49984 by behi83417@gmail.com last updated on 12/Dec/18 Commented by behi83417@gmail.com last updated on 12/Dec/18 $${A}\overset{\bigtriangleup} {{B}C},{equilateral}.{AB}={a},{A}\overset{} {{C}E}=\alpha. \\ $$$${find}:{AD},{BD},{in}\:{terms}\:{of}\:{a}\:{and}\:\:\alpha. \\ $$ Answered by…

Question-181051

Question Number 181051 by mr W last updated on 20/Nov/22 Answered by a.lgnaoui last updated on 21/Nov/22 $${cote}\:{du}\:{carre}\:{bleu}\:\left[{CD}\right]={b}\:{comme}\:{il} \\ $$$${apparait}\:{dans}\:\left({image}\right){est} \\ $$$${CD}:{prolongement}\:{de}\left[\:{AC}\right]\left({AC}\right) \\ $$$$\left[{CD}\right]=\mathrm{2}×{AC} \\…

Question-181055

Question Number 181055 by Acem last updated on 21/Nov/22 Commented by Acem last updated on 21/Nov/22 $$\ast\:{DABC} \\ $$$${Please},\:{the}\:{comments}\:{section}\:{is}\:{only} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{for} \\ $$$$\:\:\:\:\:\boldsymbol{{inquiries}}\:\boldsymbol{{and}}\:\boldsymbol{{clarifications}} \\ $$$$…