ABSTRACT
Maximum at (−0.8,8.2) 3. x = 1 4. x = −2.0,0.4 or 2.6 5. x = −1.2,0.70 or 2.5 6. x = −2.3,1.0 or 1.8 7. x = −1.5
1. 82◦27′ 2. 27◦54′ 3. 51◦11′ 4. 100◦6′52′′ 5. 15◦44′17′′ 6. 86◦49′1′′ 7. 72.55◦ 8. 27.754◦ 9. 37◦57′ 10. 58◦22′52′′
1. reflex 2. obtuse 3. acute 4. right angle 5. (a) 21◦ (b) 62◦23′ (c) 48◦56′17′′ 6. (a) 102◦ (b) 165◦ (c) 10◦18′49′′ 7. (a) 60◦ (b) 110◦ (c) 75◦ (d) 143◦ (e) 140◦
(f ) 20◦ (g) 129.3◦ (h) 79◦ (i) 54◦
8. (a) 1 & 2 6 & 8 (b) 1 & 2 & 3, 3 4, 4 6, 6 & 7, 7 & 8, 8 & 5, 3 & 8, 1 & 6, 4 & 7 or 2 & 5 (c) 1 & 5, 2 & 6, 4 & 8, 3 & 7 (d) 3 & 5 or 2 & 8
9. 59◦20′ 10. a = 69◦,b = 21◦,c = 82◦ 11. 51◦ 12. 1.326 rad 13. 0.605 rad 14. 40◦55′
1. (a) acute-angled scalene triangle (b) isosceles triangle (c) right-angled isosceles triangle (d) obtuse-angled scalene triangle (e) equilateral triangle (f) right-angled triangle
2. a = 40◦,b = 82◦,c = 66◦, d = 75◦, e = 30◦, f = 75◦
3. DF, DE 4. 52◦ 5. 122.5◦
6. φ = 51◦,x = 161◦ 7. 40◦,70◦,70◦,125◦, isosceles 8. a = 18◦50′,b = 71◦10′,c = 68◦,d = 90◦,
e = 22◦, f = 49◦,g = 41◦ 9. a = 103◦,b = 55◦,c = 77◦,d = 125◦,
e = 55◦, f = 22◦,g = 103◦,h = 77◦, i = 103◦, j = 77◦,k = 81◦
10. 17◦ 11. A = 37◦,B = 60◦,E = 83◦
1. (a) congruent BAC, DAC (SAS) (b) congruent FGE, JHI (SSS) (c) not necessarily congruent (d) congruent QRT, SRT (RHS) (e) congruent UVW, XZY (ASA)
2. proof
1. x = 16.54mm, y = 4.18mm 2. 9cm,7.79cm 3. (a) 2.25cm (b) 4 cm 4. 3m
1-5. Constructions – see similar constructions in worked Problems 30 to 33 on pages 201-203.
