Basic Engineering Mathematics, Fifth Edition

168 Basic Engineering Mathematics Thus, 49 ◦is an acute angle. (c) An angle equal to 90◦is called aright angle. (d) Any angle gr ...

Angles and triangles 169 Problem 13. Determine angleβin Figure 20.7 1338   Figure 20.7 α= 180 ◦− 133 ◦= 47 ◦(i.e. supplementar ...

170 Basic Engineering Mathematics State the general name given to an angle of 90 ◦. Determine the angles complementary to the f ...

Angles and triangles 171 20.3 Triangles Atriangleis a figure enclosed by three straight lines. The sum of the three angles of a ...

172 Basic Engineering Mathematics A right-angled triangleABCis shown in Figure 20.19. The point of intersection of two lines is ...

Angles and triangles 173 62  15  A B D E C   Figure 20.23 In triangleABC,∠A+∠B+∠C= 180 ◦(the angles in a triangle add up to ...

174 Basic Engineering Mathematics Find the anglesatofin Figure 20.27. 1058 1058 d e f (c) 328 114° b c (b) 578 (^838) a (a) Fi ...

Angles and triangles 175 (a) (b) 568299 148419 a b 688 1318 c d e g f Figure 20.32 Find the unknown angles a to k in Figure 20. ...

176 Basic Engineering Mathematics Problem 25. In Figure 20.36, trianglePQRis isosceles withZ, the mid-point ofPQ. Prove that tri ...

Angles and triangles 177 508 708 c 5 12.0cm B a C A 508 608 f 5 5.0cm d 5 4.42cm E F D Figure 20.39 In triangleABC, 50 ◦+ 70 ◦+∠ ...

178 Basic Engineering Mathematics Problem 29. A rectangular shed 2m wide and 3m high stands against a perpendicular building of ...

Angles and triangles 179 20.6 Construction of triangles To construct any triangle, the followingdrawing instru- ments are needed ...

180 Basic Engineering Mathematics B AX A^9 Q C P S Z U V R Y Figure 20.50 With reference to Figure 20.50: (i) Draw a straight li ...

Chapter 21 Introduction to trigonometry 21.1 Introduction Trigonometry is a subject that involves the measurement of sides and a ...

182 Basic Engineering Mathematics PQRis a 3, 4, 5 triangle. There are not many right- angled triangles which have integer values ...

Introduction to trigonometry 183 nearest centimetre, runs from the top of the tent to the peg? In a triangle ABC, ∠B is a right ...

184 Basic Engineering Mathematics SOHindicatessin=opposite÷hypotenuse CAHindicatescos=adjacent÷hypotenuse TOAindicatestan=opposi ...

Introduction to trigonometry 185 B A 0 2 4 (a) (b) 68 8 f(x) 7 6 4 3 2 B A C 0 2 468 8 f(x) 7 6 4 3 2  Figure 21.13 (a) PointsA ...

186 Basic Engineering Mathematics and if tanA= 3 .5984 thenA=tan−^13. 5984 =74.47◦ each correct to 2 decimal places. Use your ca ...

Introduction to trigonometry 187 Problem 16. In triangleEFGin Figure 21.16, calculate angleG E F G 2.30cm 8.71cm Figure 21.16 Wi ...