Understanding Engineering Mathematics

In Figure 5.11 AOCand COBare supplementary. An angle of 90°is a rotation through a quarter circle and is called aright angle. ...

Solution to review question 5.1.2 A.(a) A full revolution is 360°, so a fraction (12 ➤ ) p q of a full revolution is p q 360 °, ...

to the opposite sideBC– see Figure 5.14. Since we already know that for two parallel lines, alternate angles are equal, then we ...

5.2.4 Congruent triangles ➤ 144 161➤ We often need to compare pairs of triangles. Two triangles are calledcongruentif they are i ...

AngleBAClooks like a right angle, but this doesn’t mean that it is. In fact in this case itis, because, as you may have noticed, ...

A C PDM B AP = Altitude AM = Median AD = Angle bisector Figure 5.17Altitude, median and angle bisector. So the angle bisector th ...

We can see that this works by checking it for a few simple triangles – the 3 : 4 : 5 being the classic example. But this is not ...

5.2.9 Lines and angles in a circle ➤ 146 163➤ Figure 5.20 reminds you of the main definitions relating to a circle. Centre Centr ...

the anglesubtended by the minor arcABat the centreOisAOB.Wesaytheangle ACBstands on the minor arcAB, which is said tosubtendan ...

A tangent to a circle is perpendicular to the radius drawn through the point of contact. O Figure 5.23Tangent perpendicular to ...

Solution to review question 5.1.9 (i) Referring to Figure 5.8,a= 360 °− AOB,and AOB= 2 ACB= 2 × 40 °= 80 °.Soa= 280 °. (ii) E ...

Solution to review question 5.1.10 (i) In Figure 5.9(i) we haveBAD+ BCD= 180 °=a+ 125 °.Soa= 55 °by supplementary angles in a ...

B. Determine all the angles in triangles with the following angles and opposite external angles respectively (i) 25°, 114° (ii) ...

5.3.5 Similar triangles ➤➤ 145 152 ➤ A.The trianglesABCandPQRare similar. Find the lengths of all sides ofPQRfor the values ofxg ...

5.3.7 The angle bisector theorem ➤➤ 145 153 ➤ Find the missing lengthsx,y,z,u,v: (iii) (iv) (ii) A u 1 1.7 C 0.8 DDB A C B D z 2 ...

(iv) C A B a 4 a O (i) C C A A D B D a B a d O (iii) O A DB (ii) O C a d c 35 ° 40 ° 70 ° 100 ° D.Determine the labelled angles: ...

E. An equilateral triangle of side 30 cm circumscribes a circle. Find the radius of the circle. F.A circle of unit radius is ins ...

bank, a pole can be set atJ on the intersection of the linesEGand HCproduced backwards. Show thatJG=FH. (c) The lineABcrosses th ...

Find the difference in level between the floor of the cutting and the top of the bank on each side. Answers to reinforcement exe ...

5.3.3 Triangles and their elementary properties A. Other angle External angle (i) 103 ° 77 ° (ii) 86 ° 94 ° (iii) 144 ° 36 ° (iv ...