Higher Engineering Mathematics, Sixth Edition

98 Higher Engineering Mathematics

Now try the following exercise

Exercise 44 Further problems on the

theorem of Pythagoras

1. In a triangleCDE,D= 90 ◦,CD= 14 .83mm
   andCE= 28 .31mm. Determine the length of
   DE. [24.11mm]


2. 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◦]


3. 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]


4. 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]


5. 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]


6. 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

7. 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