Understanding Engineering Mathematics

5.3.7 The angle bisector theorem

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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 2.5

1.1

(i)

A

C B

y

x

D 1

2

A

v

1.7

C 1.8 B

2

5.3.8 Pythagoras’ theorem

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A.Regarding the pairs of lengths given in (i) to (v) as the (a) shortest (b) longest sides
of a right angled triangle (in consistent units) determine the third side in each case.
Leave your answers in surd form.

(i) 3, 5 (ii) 5, 12 (iii) 24, 25 (iv) 8, 17 (v) 3, 4

B.Determine the longest rod that may be placed in a rectangular box of edges 3, 4,

6 units.

5.3.9 Lines and angles in a circle

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A.A,B,Care three points on a circle centreO, taken clockwise in that order. Given the
following angles, determine the others named.

(i) ACB= 35 °, AOB (ii) ACB= 70 °,AOB

(iii) AOB= 60 °,ACB (iv) AOB= 86 °,ACB

B. Referring to QuestionAnow assume the pointsA,B,Care such thatAC=BC.For
each case specified in QuestionA, determine all angles in the trianglesAOC,AOB
andBOC.

C.Determine the angles labelled with a letter: