Basic Engineering Mathematics, Fifth Edition

194 Basic Engineering Mathematics

12. In Figure RT8.7, determine anglesx,yandz.
    (3)

598

y z

x

378

Figure RT8.7

13. In Figure RT8.8, determine anglesatoe.(5)

c e

a b d

608

1258

Figure RT8.8

14. In Figure RT8.9, determine the length ofAC.
    (4)

D A

C

E

B

3m

10m

8m

Figure RT8.9

15. In triangleJKLin Figure RT8.10, find
    (a) the lengthKJcorrect to 3 significant figures.
    (b) sinLand tanK, each correct to 3 decimal
    places. (4)

K

J L

11.60

5.91

Figure RT8.10

16. Two ships leave a port at the same time. ShipX
    travels due west at 30km/handshipYtravels due
    north.After4hoursthetwoshipsare130kmapart.
    Calculate the velocity of shipY.(4)


17. If sinA=
    12
    37

,findtanAin fraction form. (3)

18. Evaluate 5tan62◦ 11 ′ correct to 3 significant
    figures. (2)


19. Determinetheacuteanglecos−^10 .3649indegrees
    and minutes. (2)


20. In trianglePQRin Figure RT8.11, find angleP
    in decimal form, correct to 2 decimal places. (2)
    P Q

R

29.6 15.2

Figure RT8.11

21. Evaluate, correct to 3 significant figures,
    3tan81. 27 ◦−5cos7. 32 ◦−6sin54. 81 ◦.(2)


22. In triangleABCin Figure RT8.12, find lengths
    ABandAC, correct to 2 decimal places. (4)
    A

B 6 C

408 359

Figure RT8.12

23. From a pointP, the angle of elevation of a 40m
    high electricity pylon is 20◦. How far is pointP
    from the base of the pylon, correct to the nearest
    metre? (3)