lg 3 h 7.2, 8 1 7.2 Right Tringle Trig ) Use of clcultor sin 10 = sin x =.4741 c ) rete right tringles π 1) If = nd = 25, find 6 c 2) If = 30, nd = 45, = 1 find nd c 3) If in right, with right ngle t, = 70, = 35 find ) ngle of elevtion is the ngle etween the horizontl nd the line of sight to the top of n oject. ngle of depression is determined y the horizontl line down to the line of sight. d 1) How tll is tree whose shdow is 47 long when the ngle of elevtion of the sun is 49. 3. e
lg 3 h 7.2, 8 2 2) One of the two congruent sides of n isosceles tringle is 23 cm nd the vertex ngle is 43. How long is the se? 3) lloon is floting etween 2 people 50 prt. The ngle of elevtion of the lloon from one is 63.5 nd the ngle of elevtion from the other is 32.6. How high is the lloon?
lg 3 h 7.2, 8 3 lger 3 ssignment # 18 (1) Solve ech of the following right tringles plese. Express ll sides nd ngles correct to two deciml plces. () = 5.7, = 6.9, γ = 90 (c) c = 11.5, α = 51.6, γ = 90 () = 13.32, α = 18.7, γ = 90 (d) = 20, c = 29, γ = 90 (2) The digonls of rectngle mesure 18 nd intersect t n ngle of 46.6. Find the dimensions of the rectngle plese. (3) mn is stnding 100 feet from the se of tll uilding. There is lrge flgpole ner the edge of the uilding. He mesures the ngles of elevtion to the top nd ottom of the flgpole to e 28.37 nd 24.70 respectively. How tll is the flgpole? (4) Ech side of rhomus mesures 12 inches. One of the ngles of the rhomus is 53.6. Find the re of the rhomus plese.
lg 3 h 7.2, 8 4 nswers (1) () c = 8.95, α = 39.56, β = 50.44 () β = 71.30, = 39.35, c = 41.55 (c) β = 38.40, = 9.01, c = 7.14 (d) = 21, α = 46.40, β = 43.60 (2) 7.12 in. y 16.53 in. (3) 8.01 feet (4) 115.90 squre inches
lg 3 h 7.2, 8 5 h 8.1 Lw of osines Wht hppens if you don t hve right tringle nd you wnt to find sides nd ngles? Lw of osines: Given info on SSS or SS you cn find the remining sides nd ngles. c (x,y) y < is in stndrd position nd is on the xis x D x (,0)
lg 3 h 7.2, 8 6 (x,y) re of Tringle Let K = re y c K = 1 y y y sin = 2 c K = 1 2 csin K = 1 2 csin K = 1 2 Sin x D x (,0) EX. Find the re of the tringle, 12 110 8 cm
lg 3 h 7.2, 8 7 Heron s Formul: s = 1 2 ( + + c ) K = s ( s )( s )( s c ) (no ngles!) Find the re of the tringle: 17 9 10 cm Lw of Sines sin = y c S, S sin = y c (sin ) = (sin c x (x,y) y D (,0) sin sin sin = = c ex. Find if = 30, = 45, nd = 8 ex. Find if = 60, c = 75, nd = 15 ex. To the nerest meter, find the distnce cross the pond if 108 39 950 m
lg 3 h 7.2, 8 8 8.2 Lw of Sines SS Three cses Think of wrecking ll where one side nd one ngle re set. se 1: no solution (not possile) (error messge) < h h se 2: one solution, two wys = h h = h se 3: two solutions h < < h Ex. Solve if = 50, = 65 nd = 57 (SS) sin = sin sin57 sin = 50 65 65(sin57) = 50(sin) 54.5 = 50(sin) 1.09 = sin (not possile, 1 sin 1 ) c
lg 3 h 7.2, 8 9 Ex. Solve if = 60, = 65 nd = 57 (SS) sin = sin sin57 sin = 60 65 c Ex. Solve if c = 8, = 20 nd = 122 sin25 sin = 10 13 Summry
lg 3 h 7.2, 8 10 lger 3 ssignment # 19 (1) Solve ech of the following tringles plese. Express ll sides nd ngles correct to two deciml plces. Find the re of ech tringle. () = 2.6, = 3.1, c = 4.3 (c) α = 51, c = 18, = 25 () = 14, c = 8.1, β = 58.2 (d) = 7, c = 9, β = 35 (2) Given the figure elow, 1 2, with sides s mrked. Find: D, D, m 1, m 3 nd m 4. 4 10.6 8.2 3 D 1 2 12.8 (3) Given the figure elow, D is trpezoid with D nd with sides nd ngle s mrked. Find:, D,, nd m. 6.4 8.8 D 56.2 14.2 (4) Sketch grph of the lines y = 2x 1 nd y = x + 1 on the sme xis. Find the mesure of the cute ngle formed t the point of intersection of the lines.
lg 3 h 7.2, 8 11 nswers (1) () α = 36.82, β = 45.62, γ = 97.56, re = 3.99 () α = 86.52, γ = 35.28, = 11.92, re = 48.19 (c) β = 94.98, γ = 34.02, = 32.05, re = 224.15 (d) α = 97.48, γ = 47.52, = 12.10, re = 31.23 or α = 12.52, γ = 132.48, = 2.65, re = 6.83 (2) D = 4.14, D = 8.84, m 1 = 27.78, m 3 = 67.42, m 4 = 84.8 (3) = 11.83, D = 13.46, = 7.87, m = 68.33 (4) 18.43
lg 3 h 7.2, 8 12 lger 3 Review Worksheet ssignment # 20 (1) Solve ech of the following tringles plese. Express ll sides nd ngles correct to two deciml plces. Find the re of ech tringle. () = 7.8, = 6.3, γ = 90 (c) = 14, = 19, γ = 43 () = 5.3, = 7.2, c = 10.4 (d) α = 62, β = 23, c = 8.5 (2) Given the figure to the right, DE is regulr pentgon inscried in circle whose rdius is 10. Find the perimeter nd re of the pentgon plese E D (3) Given the figure elow with sides nd (4) ngles s indicted, find, D,, m D, nd m. Given the figure elow, D is prllelogrm with sides nd ngle s mrked. Find D, nd m. 58 8.6 10 5.2 42.1 4.6 D 55 D
lg 3 h 7.2, 8 13 nswers (1) () c = 10.03, α = 51.07, β = 38.93, re = 24.57 () α = 28.26, β = 40.03, γ = 111.71, re = 17.73 (c) α = 47.45, β = 89.55, c = 12.96, re = 90.71 (d) γ = 95, = 7.53, = 3.33, re = 12.50 (2) perimeter = 58.78, re = 237.76 (3) = 11.24, D = 10.35, = 12.86, m D = 19.22, m = 47.80 (4) D = 11.72, = 8.04, m = 113.99
lg 3 h 7.2, 8 14 1. Solve the following right tringles ( is the right ngle). ) = 2, = 7 ) m = 16º, c = 14 c) m = 64º, c = 19.2 d) = 9, m = 49º e) m = 30º, = 11 2. Solve the following tringles completely. ) m = 49º, m = 57º, = 8 ) m = 83º, = 80, = 70 c) m = 70º, m = 58º, = 84 d) = 5, =6, c = 7 e) m = 47º, = 20, = 24 f) m = 95º, = 6, = 8 g) m = 58º, = 26, = 29 3. shdow 30 m long is thrown from tree. If the ngle of depression of the sun is 65º, how tll is the tree? 4. The ngle of elevtion from point on the ground to the top of uilding is 38º. From point 50 ft closer, the ngle of elevtion is 45º. How tll is the uilding? 5. tree is roken y the wind. The top touches the ground 13 m from the se of the tree. It (the roken rnch) mkes n ngle with the ground of 29º. How tll ws the tree? 6. tringulr lot fces 2 streets tht meet t n ngle of 85º. The sides of the lot fcing the streets re ech 160 ft. Find the perimeter of the lot. 7. Two plnes leve n irport t the sme time, ech flying 110 mi/hr. One flies 60º est of north, the other flies 40º est of south. How fr prt re the plnes fter 3 hours? 8. The sides of tringle re 6.8 cm, 8.4 cm nd 4.9 cm. Find the mesure of the smllest ngle. 9. 40 ft ntenn stnds on top of uilding. From the ground, the ngles of elevtion of the top nd ottom of the ntenn re 56º nd 42º respectively. How tll is the uilding? Prt 2 1. lloon is floting etween two oservers who re 220 feet prt. The ngle of elevtion of the lloon from oserver one is 67º nd from oserver two is 31º. How fr is the lloon from oserver one? 2. To find the distnce cross cnyon, surveying tem loctes points nd on one side of the cnyon nd point on the other side of the cnyon. The distnced etween nd is 85 yrds. m is 68º nd m is 88º. Find the distnce cross the cnyon. 3. The longer side of prllelogrm is 6.00 meters. m = 56º nd m α= 35º. Find the length of the longer digonl. α 4. Two oservers in line directly under kite, nd 30 ft. prt, oserve the kite t ngle of elevtions of 62º nd 78º respectively. Find how high the kite is in the ir. 5. 35 foot high telephone pole is situted on n 11º slope from. The ngle of elevtion from point to the top of the pole is 32º. Find the length of the wire.
lg 3 h 7.2, 8 15 6. surveying tem determines the height of hill y plcing 23 ft pole t the top nd mesuring the ngles of elevtion to the ottom nd the top of the pole. If they re 70º nd 75º respectively, find the height of the hill. 7. developer hs tringulr lot t the intersection of two streets. The streets meet t n ngle of 72º nd the lot hs 300 ft of frontge long one street nd 416 ft of frontge long the other street. Find the length of the third side of the lot. 8. The sides of tringulr city lot hve sides of 224 ft, 182 ft nd 165 ft. Find the smllest ngle. 9. Find the numer of cres in psture whose shpe is tringle with sides 800 ft, 1020 ft nd 680 ft. (Hmm how mny squre feet in n cre?) nswers: ) c=7.28, m =15.9, m =74.1 ) m = 74, = 3.86, = 13.5 c) m = 26, = 8.42, = 17.3 d) = 10.3, c = 13.7, m = 41º e) m = 60, = 19.1, c = 2.2 2. Solve the following tringles completely. ) m = 74º, = 8.89, c = 10.2, = 34,2 ) m = 60.3º, m = 36.7, c = 48.2, = 1670 c) m = 52º, = 100, c = 90.4, 3570 d) m = 44.4, m 57.1, m = 78.5, = 14.7 e) m = 37.6º, m = 95.4, c = 32.7, = 239 f) no tringle g) m = 71.1, m = 50.9, c = 23.8, = 293 m = 108.9, m = 13.1, c = 6.95, = 85.4 3. h = 64.3 4. h = 179 ft 5. h = 22.1 m 6. p = 536 ft 7. d = 424 mi 8. 35.7 9. h = 61.9 ft Prt 2 1. 114 ft 2. 194 yd 3. 8.67 m 4. 40.3 ft 5. 95.9 ft. 6. 64.2 ft 7. 431 ft 8. 46.5 9. 271558 squre ft = 6.23 cres
lg 3 h 7.2, 8 16 1. lloon is floting etween two oservers who re 220 feet prt. The ngle of elevtion of the lloon from oserver one is 67º nd from oserver two is 31º. How fr is the lloon from oserver one? 2. To find the distnce cross cnyon, surveying tem loctes points nd on one side of the cnyon nd point on the other side of the cnyon. The distnced etween nd is 85 yrds. m is 68º nd m is 88º. Find the distnce cross the cnyon. 3. The longer side of prllelogrm is 6.00 meters. m = 56º nd m α= 35º. Find the length of the longer digonl. α 4. Two oservers in line directly under kite, nd 30 ft. prt, oserve the kite t ngle of elevtions of 62º nd 78º respectively. Find how high the kite is in the ir. 6. surveying tem determines the height of hill y plcing 23 ft pole t the top nd mesuring the ngles of elevtion to the ottom nd the top of the pole. If they re 70º nd 75º respectively, find the height of the hill. 7. developer hs tringulr lot t the intersection of two streets. The streets meet t n ngle of 72º nd the lot hs 300 ft of frontge long one street nd 416 ft of frontge long the other street. Find the length of the third side of the lot. 8. The sides of tringulr city lot hve sides of 224 ft, 182 ft nd 165 ft. Find the smllest ngle. 9. Find the numer of squre feet in psture whose shpe is tringle with sides 800 ft, 1020 ft nd 680 ft. nswers: 1. 114 2. 194 3. 8.67 4. 40.3 6. 64.2 7. 431 8. 46.5 9 re= 271558