98 Higher Engineering Mathematics
Now try the following exercise
Exercise 44 Further problems on the
theorem of Pythagoras
- In a triangleCDE,D= 90 ◦,CD= 14 .83mm
andCE= 28 .31mm. Determine the length of
DE. [24.11mm] - TrianglePQRis isosceles,Q being a right
angle. If the hypotenuse is 38.47cm find (a)
the lengths of sidesPQandQR, and (b) the
value of∠QPR. [(a) 27.20cm each (b) 45◦] - A man cycles 24km due south and then 20km
due east. Another man, starting at the same
time as thefirst man, cycles 32kmdue east and
then7kmduesouth.Findthedistancebetween
the two men. [20.81km] - A ladder 3.5m long is placed against a perpen-
dicular wall with its foot 1.0m from the wall.
How far up the wall (to the nearest centimetre)
does the ladder reach? If the foot of the lad-
der is now moved 30cm further away from the
wall, how far does the top of the ladder fall?
[3.35m,10cm] - Two ships leave a port at the same time. One
travels due west at 18.4km/hand the other due
south at 27.6km/h. Calculate how far apart the
two ships are after 4hours. [132.7km] - Figure 11.4 shows a bolt rounded off at one
end. Determine the dimensionh. [2.94mm]
R 5 45mm
h
r^5
16mm
Figure 11.4
- Figure 11.5 shows a cross-section of a
component that is to be made from a round bar.
If the diameter of the bar is 74mm, calculate
the dimensionx. [24mm]
72mm
74mm
x
Figure 11.5
11.3 Trigonometric ratios of acute angles
(a) With reference to the right-angled triangle shown
in Fig. 11.6:
(i) sineθ=
opposite side
hypotenuse
i.e. sinθ=
b
c
(ii) cosineθ=
adjacent side
hypotenuse
i.e. cosθ=
a
c
(iii) tangentθ=
opposite side
adjacent side
i.e. tanθ=
b
a
(iv) secantθ=
hypotenuse
adjacent side
i.e. secθ=
c
a
(v) cosecantθ=
hypotenuse
opposite side
i.e. cosecθ=
c
b