Teoram Phythagoras
A bheil fios agad air faid dà thaobh ann an triantan ceart-cheàrnach?
A bheil agad ri faid an 3mh taobh obrachadh a-mach?
Feumaidh tu teoram Phythagoras!
A rèir teoram Phythagoras, ann an triantan ceart-cheàrnach tha a' hypotenuse ceàrnagaichte co-ionann ri sùim ceàrnagaichte an dà thaoibh eile.
Tha e nas fhasa seo a sgrìobhadh mar: \(a^{2} = b^{2} + c^{2}\)
A' sgrìobhadh co-aontar le teoram Phythagoras
Sgrìobh teoram Phythagoras airson nan triantain gu h-ìosal.
\(a^{2} = b^{2} + c^{2}\)
\(e^{2} = d^{2} + f^{2}\)
\(m^{2} = s^{2} + t^{2}\)
Ag obrachadh a-mach faid a' hypotenuse
Eisimpleir
Cleachd teoram Phythagoras airson faid a' hypotenuse obrachadh a-mach. Thoir do fhreagairt gu 2 ionad dheicheach.
Sgrìobh an co-aontar: \(x^{2} = 7^{2} + 4^{2}\)
Ceàrnagaich na faidean air a bheil fios agad: \(x^{2} = 49 + 16\)
Cuir-ris iad: \(x^{2} = 65\)
Lorg am freumh ceàrnagach: \(x = \sqrt {65}\)
\(= 8.06\ (gu\ 2\ id)\)
Ceistean
Feuch a-nis na ceistean seo.
\(x^{2} = 6^{2} + 10^{2}\)
\(x^{2} = 36 + 100\)
\(x^{2} = 136\)
\(x = \sqrt {136}\)
\(= 11.66\ (gu\ 2\ id)\)
\(a^{2} = 5^{2} + 11^{2}\)
\(a^{2} = 25 + 121\)
\(a^{2} = 146\)
\(a = \sqrt {146}\)
\(= 12.08\ (gu\ 2\ id)\)
\(s^{2} = 1.4^{2} + 2.5^{2}\)
\(s^{2} = 1.96 + 6.25\)
\(s^{2} = 8.21\)
\(s = \sqrt {8.21}\)
\(= 2.87\ (gu\ 2\ id)\)
Ma fhuair thu iad sin ceart, chleachd thu teoram Phythagoras ceart airson faid a' hypotenuse obrachadh a-mach.
Ag obrachadh a-mach faid taobh nas giorra
Ciamar a chleachdas sinn teoram Phythagoras airson faid fear de na taobhan as giorra obrachadh a-mach?
Eisimpleir
Obraich a-mach faid an taoibh a tha comharraichte le \(a\).
Thoir do fhreagairt gu 2 ionad dheicheach.
Sgrìobh an co-aontar: \(12^{2} = a^{2} + 8^{2}\)
Ath-rèitich an co-aontar: \(a^{2} = 12^{2} - 8^{2}\)
Ceàrnagaich faidean nan taobhan air a tha fios agad: \(a^{2} = 144 - 64\)
Thoir-air-falbh: \(a^{2} = 80\)
Lorg am freumh ceàrnagach: \(a = \sqrt {80}\)
\(a = 8.94\ (gu\ 2\ id)\)
Ceistean
Feuch a-nis na ceistean seo.
\(14^{2} = a^{2} + 9^{2}\) (Chan fheum thu a' chiad loidhne seo a shealltainn nad obrachadh)
\(a^{2} = 14^{2} - 9^{2}\)
\(a^{2} = 196 - 81\)
\(a^{2} = 115\)
\(a = \sqrt {115}\)
\(= 10.72\ (gu\ 2\ id)\)
\(20^{2} = r^{2} + 11^{2}\)
\(r^{2} = 20^{2} - 11^{2}\)
\(r^{2} = 400 - 121\)
\(r^{2} = 279\)
\(r = \sqrt {279}\)
\(= 16.70\ (gu\ 2\ id)\)
\(3.8^{2} = e^{2} + 2.4^{2}\)
\(e^{2} = 3.8^{2} - 2.4^{2}\)
\(e^{2} = 14.44 - 5.76\)
\(e^{2} = 8.68\)
\(e = \sqrt {8.68}\)
\(= 2.95\ (gu\ 2\ id)\)
A' fuasgladh cheistean le teoram Phythagoras
Eisimpleir
Tha post \(30\ m\) a dh'àirde.
Tha càball ceangailte ri mullach a' phuist.
Tha ceann eile a' chàbaill \(14\ m\) bho bhonn a' phuist.
A rèir nan riaghailtean feumaidh an càball a bhith nas lugha na \(35\ m\) a dh'fhaid.
A bheil an càball a rèir nan riaghailtean?
Thoir adhbhar airson do fhreagairt.
\(x^{2} = 30^{2} + 14^{2}\)
\(x^{2} = 900 + 196\)
\(x^{2} = 1096\)
\(x = \sqrt {1096}\)
\(x = 33.1\ (gu\ 1\ id)\)
Tha seo a rèir nan riaghailtean oir tha \(33.1\ m\) nas lugha na \(35\ m\).
Feumaidh tu d' adhbhar a choimeas ris an riaghailt sa cheist.
Ceist
Feumaidh sail fo mhullach taighe a bhith co-dhiù \(2\ m\) a dh'àirde.
Am biodh sail suidhichte mar a tha san diagram ceart gu leòr?
Thoir adhbhar airson do fhreagairt.
\(4^{2} = x^{2} + 3.5^{2}\)
\(x^{2} = 4^{2} - 3.5^{2}\)
\(x^{2} = 16 - 12.25\)
\(x^{2} = 3.75\)
\(x = \sqrt {3.75}\)
\(x = 1.936\ (gu\ 3\ id)\)
Cha bhitheadh. Cha bhiodh seo freagarrach oir tha 1.936 nas lugha na 2.
