Basic Engineering Mathematics, Fifth Edition

208 Basic Engineering Mathematics from which e= √ 1082. 85 = 32 .91mm=DF Applying the sine rule, 32. 91 sin64◦ = 25. 0 sinF from ...

Non-right-angled triangles and some practical applications 209 Now try the following Practice Exercise PracticeExercise 91 Solut ...

210 Basic Engineering Mathematics 458 V 25 100V V 15 40V A O B Figure 23.11 AngleOBA= 180 ◦− 45 ◦= 135 ◦ Applying the cosine rul ...

Non-right-angled triangles and some practical applications 211 28.5 m (^728) 34.6 m 52.4 m^758 Figure 23.14 Determine the lengt ...

212 Basic Engineering Mathematics (a) Applying the sine rule, AB sin50◦ = AO sinB from which sinB= AOsin50◦ AB = 10 .0sin50◦ 30. ...

Non-right-angled triangles and some practical applications 213 B C A 408 Figure 23.20 From Figure 23.20, determine how farC mov ...

Chapter 24 Cartesian and polar co-ordinates 24.1 Introduction There are two ways in which the position of a point in a plane can ...

Cartesian and polar co-ordinates 215 Hence, (3, 4) in Cartesian co-ordinates corre- sponds to (5, 53.13◦) or (5, 0.927 rad) in p ...

216 Basic Engineering Mathematics 24.3 Changing from polar to Cartesian co-ordinates y y O x Q x P r  Figure 24.6 From the righ ...

Cartesian and polar co-ordinates 217 Now try the following Practice Exercise PracticeExercise 95 Changing polar to Cartesianco-o ...

Revision Test 9 : Trigonometric waveforms and practicaltrigonometry This assignment covers the material contained in Chapters 22 ...

Chapter 25 Areas of common shapes 25.1 Introduction Areais a measure of the size or extent of a plane surface. Area is measured ...

220 Basic Engineering Mathematics (a) (b) (c) (d) (e) (f) Figure 25.1 A B D C Figure 25.2 P Q S R P Q S R Figure 25.3 W Z Y X Fi ...

Areas of common shapes 221 In triangleFGH,40◦+ 90 ◦+b= 180 ◦, since the angles in a triangle add up to 180◦, from which b= 50 ◦. ...

222 Basic Engineering Mathematics Table 25.1Formulae for the areas of common shapes Area of plane figures Square x x Area=x^2 Re ...

Areas of common shapes 223 Area of rectangle=l×b= 7. 0 × 4. 5 = 31 .5cm^2 Perimeter of rectangle= 7 .0cm+ 4 .5cm + 7 .0cm+ 4 .5c ...

224 Basic Engineering Mathematics Problem 7. A rectangular tray is 820mm long and 400mm wide. Find its area in (a) mm^2 (b) cm^2 ...

Areas of common shapes 225 Total area of brickwork= 48 + 12 =60m^2. Now try the following Practice Exercise PracticeExercise 97 ...

226 Basic Engineering Mathematics Determine the area of an equilateral triangle of side 10.0cm. If paving slabs are produced in ...

Areas of common shapes 227 inthe middleof the garden. Find, correct tothe nearest square metre, the area remaining. Determine t ...