Mehlala ea Lipotso Tse Buisanang ka Litekanyetso tsa Trigonometric ho Liphiramide
Pendahuluan
Ha e le hantle, trigonometry ke lekala la lipalo le ithutang likamano pakeng tsa likhutlo le mahlakore a likhutlotharo. Likarolelano tsa trigonometry li bohlokoa mafapheng a fapaneng a kang fisiks, boenjiniere, esita le meralo ea meaho. E 'ngoe ea mehlala e metle ka ho fetisisa ea tšebeliso ea trigonometry meralong ea meaho ke Lipiramite tsa Egepeta. Sehloohong sena, re tla tšohla likarolelano tsa trigonometry re sebelisa mehlala e amanang le lipiramite.
Selelekela sa Trigonometry Liphiramideng
Lipiramide tsa Baegepeta, haholo-holo Lipiramide tsa Giza, ke meaho e tummeng haholo 'me e bile taba e ithutoang ke litsebi tse ngata tsa lipalo le litsebi tsa meralo. E 'ngoe ea likarolo tsa bohlokoa tsa piramide ke khutlotharo. Likhutlotharo li ka fumanoa liponong tsa profil le likarolong tse fapaneng.
Ho tsoa phiramiting, re ka fumana dikhutlotharo tse sekametseng ka ho le letona, dikhutlotharo tse lekanang, le dibopeho tse ding tse fapaneng tsa dikhutlotharo. Tshebediso ya trigonometry e thusa haholo ho fumana boholo, bophahamo le moepa wa phiramiti.
Mohlala oa mathata
Potso ea 1: Ho Bala Bophahamo ba Phiramide
"A re re piramite e na le bolelele ba motheo ba limithara tse 150 le moeli o sekametseng (apothem) oa limithara tse 130. Bolelele ba piramite ke bofe?"
Puisano:
Bothateng bona, re fuoa hypotenuse le bolelele ba motheo oa piramite. Ho bala bophahamo ba piramite, re ka sebelisa khopolo-taba ea Pythagorean. Piramite e ka aroloa ka likhutlotharo tse peli tse nepahetseng.
1. Re hloka ho fumana halofo ea bolelele ba lehlakore la motheo ho etsa khutlotharo e nepahetseng.
\( \text{Bolelele ba halofo ya lehlakore la motheo} = \frac{150}{2} = 75 \text{meters} \)
2. Rea tseba hore:
\( a^2 + b^2 = c^2 \)
moo \(a\) e leng halofo ea bolelele ba lehlakore la motheo, \(b\) ke bophahamo ba piramite, 'me \(c\) ke hypotenuse.
3. Kenya linomoro ka har'a equation:
\( 75^2 + b^2 = 130^2 \)
4. Bala:
\( 5625 + b^2 = 16900 \)
\( b^2 = 16900 – 5625 \)
\( b^2 = 11275 \)
\( b = \sqrt{11275} \hoo e ka bang 106.2 \mongolo{methara} \)
Kahoo, bophahamo ba piramite bo ka ba limithara tse 106.2.
Potso ea 2: Ho Bala Sekhutlo sa ho Tšepahala ha Phiramide
"Sekhutlo sa sekamo sa apothem ea piramite ho ea botlaaseng ba piramite se nang le bolelele ba lehlakore la motheo ba limithara tse 150 le bophahamo ba limithara tse 106.2 ke sefe?"
Puisano:
Ho fumana sekhutlo sa ho sekamela (\(\theta\)) sa apothem ho ea botlaaseng ba piramite, re ka sebelisa mosebetsi oa trigonometric, e leng tangent (\(\tan\)).
1. Sebelisa foromo \(\tan(\theta) = \frac{\text{height}}{\frac{\text{base}}{2}}\).
2. Kenya linomoro:
\( \tan(\theta) = \frac{106.2}{75} \)
3. Bala:
\( \tan(\theta) \hoo e ka bang 1.416 \)
4. Fumana sekhutlo o sebedisa tangent e fapaneng (\(\tan^{-1}\)):
\( \theta = \tan^{-1}(1.416) \hoo e ka bang 54.14^\circ \)
Kahoo, sekhutlo sa ho sekamela ha apothem botlaaseng ba piramite ke hoo e ka bang di-degree tse 54.14.
Potso ea 3: Ho Bala Bolelele ba Apothem ka Sine le Cosine
"A re re piramite e bophahamo ba limithara tse 120 'me sekhutlo sa tšekamelo ea apothem ea piramite ho ea botlaaseng ke likhato tse 55. Bolelele ba apothem ke bofe?"
Puisano:
Re ka sebelisa mosebetsi oa sine kapa cosine ho rarolla bothata bona.
1. Sebelisa cosine ho e rarolla, u hopola:
\( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)
2. Lokisa equation bakeng sa Hypotenuse (apothem):
\( \text{Hypotenuse} = \frac{\text{Adjacent}}{\cos(\theta)} \)
3. Kenya linomoro:
\( \text{Hypotenuse} = \frac{120}{\cos(55^\circ)} \)
4. Bala:
\( \cos(55^\circ) \hoo e ka bang 0.5736 \)
\( \text{Hypotenuse} = \frac{120}{0.5736} \hoo e ka bang 209.3 \text{meters} \)
Kahoo, bolelele ba apothem ke limithara tse ka bang 209.3.
Qetello
Mathata a kaholimo, re sebelisitse likarohano tse fapaneng tsa trigonometric ho bala bophahamo, sekhutlo sa leralla, le bolelele ba apothem ba piramide. Ka kutloisiso ea trigonometry, re ka rarolla mathata a fapaneng a jeometri a ka 'nang a bonahala a rarahane ha re a sheba ka lekhetlo la pele. Trigonometry e fana ka sesebelisoa sa bohlokoa bakeng sa ho utloisisa le ho rarolla mathata ao re kopanang le 'ona lefatšeng la sebele, haholo-holo maemong a meralo joalo ka liphiramide tsa Baegepeta.
