Understanding Engineering Mathematics

Find the difference in level between the floor of the cutting and the top of the bank on

each side.

Answers to reinforcement exercises

5.3.1 Division of a line in a given ratio

A.Internal division(AP,PB, all in cm)

(i)

8

3

,

4

3

(ii)

12

5

,

8

5

(iii)

20

9

,

16

9

(iv)

6

5

,

14

5

(v)

2

3

,

10

3

External division(in cm)

(i) 4, 8 (ii) 8, 12 (iii) 16, 20

(iv) 3, 7 (v) 1, 5

B.Internal division(in cm)

(i) 3, 1 (ii)

10

3

,

4

3

(iii)

18

5

,

8

5

(iv)

20

3

,

14

3

(v) 12, 10

External division(in cm)

(i) 1, 1 (ii)

2

3

,

4

3

(iii)

2

5

,

8

5

(iv)

8

3

,

14

3

(v) 8, 10

5.3.2 Intersecting and parallel lines and angular measurement

(i) (ii)

50 ° 130 ° 50 ° 130 °

130 ° 50 ° 130 ° 50 °

80 ° 80 °

80 °

80 ° 80 °

80 °

100 ° 80 ° 100 ° 80 °

100 ° 100 °