Right Angle Trigonometry

Transcription

1 Righ gl Trigoomry I. si Fs d Dfiiios. Righ gl gl msurig 90. Srigh gl gl msurig 80. u gl gl msurig w 0 d omplmry gls wo gls whos sum is Supplmry gls wo gls whos sum is Righ rigl rigl wih righ gl 7. Isosls rigl rigl wih xly wo sids qul 8. Equilrl rigl rigl wih ll hr sids qul 9. Th sum of h gls of rigl is I grl, pil lrs rfr o gls whil smll lrs rfr o h sids of rigl. For xmpl, sid is opposi gl. II. Righ Trigl Fs d Exmpls. Hypous h sid opposi h righ gl, sid.. Pyhgor Thorm - +. d r omplmry. Pg of

2 III. Exmpls:. I righ rigl, h hypous is 0 ihs d o sid is 8 ihs. Wh is h lgh of h ohr sid? Soluio: ?. I righ rigl Δ, if, wh is h msur of? Soluio: Th wo u gls i righ rigl r omplmry IV. Similr Trigls:. Two rigls r similr if h gls of o rigl r qul o h orrspodig gls of h ohr. I similr rigls, rios of orrspodig sids r qul. odiios for Similr Trigls ( Δ ~ ΔEGF ). orrspodig gls i similr rigls r qul: E F F G. Rios of orrspodig sids r qul: G E EG EF FG Pg of

3 Exmpl : 50 F E 50 E 50 mrs EF m d 00 m Fid h lgh of sid. Noi h Δ d Δ EF r similr si orrspodig gls r qul. (Thr is righ gl oh F d, is h sm i oh rigls d quls h u gl E.) E EF 50 Soluio: so 00 y ross muliplyig w g: 50 ( ) (00) Thrfor 44 mrs. E 50 mrs EF m d 00 m Fid h lgh of sid. Exmpl : ll rigls r similr o o ohr. Two sids r of qul lgh d h hypous is ims h lgh of h of h qul sids ll rigls r similr o o ohr. Th shors sid of lgh is opposi h smlls gl ( 0 ). Th hypous is wi h lgh of h shors sid. Th sid opposi h 60 hs lgh ims h shorr lg. Pg of

4 Prolm: Fid h lghs of h lgs of rigl if h hypous is 8 mrs. Soluio: ) If 8, h 4 mrs d ) (4) 4 mrs. V. Th Six Trigoomri Rios for u gls si osi g opposi hypous si os s hypous si opposi dj hypous os s s hypous os dj opposi dj og o dj opposi TRIG TRIK: good wy o rmmr h rig rios is o us h mmoi SOH H TO! SOH H TO i p p o s i y p o u s o s i d j y p o u s g p p o s i d j Pg 4 of

5 Exmpl : Fid h six rigoomri rios for h u gl. Soluio: opposi si. Usig h ov dfiiios, h rs r: hypous os,, s, s, o Exmpl : I h righ Δ, d. Drmi h six rigoomri rios for. Soluio: Us Pyhgor Thorm: ± 0 (Si lgh is posiiv, w will oly us 0.) opp si hyp dj 0 opp os hyp 0 0 dj hyp 0 hyp 0 s s 0 opp dj dj o opp Pg 5 of

6 VI. Spil ss. Trigoomri vlus of 0 d 60 (Us h rigl from pg..) si 0 si 60 0 os 0 os s 0 s 60 s 0 s 60 o 0 o 60. Trigoomri vlus of 45 (Us h rigl from pg..) si 45 s 45 os 45 s o 45 Pg 6 of

7 VII. ovrig Mius d Sods o Diml Form (Nssry for mos lulor us i vluig rig vlus). To ovr from sods o diml pr of miu, divid h umr of sods y 60.. To ovr from mius o diml pr of dgr, divid h umr of mius y 60. Exmpl : ovr o dgrs usig dimls. 47 Soluio: Exmpl : ovr 5 0 o dgrs usig dimls. Soluio: VIII. Righ Trigl Trigoomry Prolms To Solv Righ Trigl Prolms: Thr r six prs o y rigl; sids d gls. Eh rig formul (x: si /) ois hr prs; o u gl d wo sids. If you kow vlus for wo of h hr prs h you solv for h hird ukow pr usig h followig mhod:. Drw righ rigl. Ll h kow prs wih h giv vlus d idi h ukow pr(s) wih lrs.. To fid ukow pr, hoos rig formul whih ivolvs h ukow pr d h wo kow prs. Pg 7 of

8 Exmpl : righ rigl hs 8 d 6. Fid h lgh of sid. Soluio: 6 8 Whih rig formuls ivolv u gl () d h sid opposi () d h sid dj () o h gl? Si oh g d og do, ihr ould usd o solv his prolm. W will us g. opp so, 6 or dj 8 8 Thrfor (lwys hk your swr y omprig siz of gl d lgh of sid; h logr sid is lwys opposi h lrgr gl.) IX. gls of Elvio d Dprssio gl of dprssio gl of lvio Exmpl: From poi 4 f from h foo of owr d o h sm lvl, h gl of lvio of h owr is 6 0. Fid h high of h owr. Soluio: h 6 0 (6.) 4 h f. h 4(0.755) h 9. f. Pg 8 of

9 Pri Prolms:. I righ rigl Δ, if 9 ihs d 6 ihs, fid.. Fid h lgh of sid. No: This prolm d digrm orrspods o fidig h high of sr ligh pol ( ) if 6 f. m ( EF ) ss shdow ( F ) of 5 f. d h pol ss shdow ( ) of 45 f. E 6 0 F 5. Evlu: F G 5 E ) si E ) E ) os F d) s F 4. Evlu: (Drw rfr d rigls) ) si 0 ) 60 ) s 60 d) 45 ) s 45 f) o 0 Pg 9 of

10 5. Evlu: 8 0 ) ) s ) o d) s 6. ovr o diml oio usig lulor: ) ) 45 7 Evlu, usig lulor: ) si 5 48 d) o Ll h sids d rmiig gls of righ rigl Δ, usig,,, d. If 4 d 7, fid h vlus of h rmiig prs. Pg 0 of

11 8. Giv righ rigl Δ wih 0. 6 d 5 40, fid. Drw digrm. 9. From liff 40 f ov h shor li, osrvr os h h gl of dprssio of ship is 0. Fid h dis from h ship o poi o h shor dirly low h osrvr. liff ship Pg of

12 swrs o Righ Trigl Trigoomry:. 5 ihs (us Pyhgor Thorm). 6 EF F ) si E ) E ) 5 os F d) s F 4. (s pr E of h hdou) ) si 0 ) 60 ) s 60 d) 45 ) s 45 f) o (us Pyhgor Thorm) ) ) s ) 6 o d) 4 5 s 4 6. ) 76. ) ) d) (Us os or s o solv for ukow ) x x 55.4f..5 (gl of dprssio) 40 liff x.5 ship Pg of