An riaghailt sine
Bidh sinn a' cleachdadh nan co-mheasan triantanachd sine, cosine agus tansaint nuair a bhios sinn ag obrachadh a-mach ³¦³ó±ðà °ù²Ôan agus thaobhan ann an triantain cheart-³¦³ó±ðà °ù²Ôach. Tha sinn a-nis a' dol a leudachadh triantanachd thairis air triantain cheart-³¦³ó±ðà °ù²Ôach agus cleachdaidh sinn e airson ceistean fhuasgladh co-cheangailte ri triantan sam bith.
\(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}}\)
Cleachdaidh sinn riaghailt sine nuair a tha fios againn air meud:
- dà thaobh agus aon ³¦³ó±ðà °ù²Ô (a tha mu choinneamh aon dhe na taobhan seo)
- aon taobh agus dà ³¦³ó±ðà °ù²Ô sam bith
Eisimpleir
Lorg meud ³¦±ðà °ù²Ô R.
\(\frac{p}{{\sin P}} = \frac{r}{{\sin R}}\)
Ionadaich am fiosrachadh bhon diagram
\(\frac{9}{{\sin (75^\circ )}} = \frac{4}{{\sin R}}\)
Cleachd 'atharraich taobh, atharraich obrachadh'.
\(9\sin R = 4\sin (75^\circ )\)
\(\sin R = \frac{{4\sin (75^\circ )}}{9}\)
\(SinR=0.429\)
Nuair a ghluaiseas tu sin chun an taoibh eile, 's e sin -1 a bhios ann.
\(R=sin^{-1}\,0.429\)
\(R = 25.4^\circ (gu\,1\,id)\)
Cuimhnich gum brùth thu 'shift' agus an uair sin 'sin' airson 'sin-1' fhaighinn air an à ireamhair agad.
A-nis feuch na ceistean gu h-ìosal.
Question
Lorg faid YZ.
Tha fios againn air dà Nuair a choinnicheas dà loidhne dhìreach, thèid ³¦±ðà °ù²Ô a chruthachadh. agus mar sin feumaidh gu bheil an treas ³¦±ðà °ù²Ô san triantan a' dèanamh \(180^\circ\) ie \(x = 45^\circ\).
\(\frac{x}{{\sin X}} = \frac{z}{{\sin Z}}\)
\(\frac{x}{{\sin (45^\circ )}} = \frac{4}{{\sin (40^\circ )}}\)
\(x = \frac{4}{{\sin (40^\circ )}} \times \sin (45^\circ )\)
\(x = \frac{{4\sin (45^\circ )}}{{\sin (40^\circ )}}\)
\(x = 4\sin (45^\circ ) \div \sin (40^\circ )\)
\(x = 4.40025...\)
Mar sin \(YZ = 4.4\,cm\,(gu\,1\,id)\)