Unit 13
Trigonometry
PRACTICE QUESTIONS: UNIT 13
1. Prove that
Solution:
Taking L.H.S
=
=
= R.H.S
Hence proved
2. Given that
Ans:
, calculate without using tables:
As Sin =
Perpendicular = 7
Hypotenuse = 25
So Base = √
=√
=√
= 24
i.
Ans:
Tan
The value of Tan , if
If is acute
is acute.
=
ii.
The value of Cos , if
Ans:
Cos
is obtuse.
-24/25
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Unit 13
Trigonometry
3. The figure below, not drawn to scale, BC = 5cm, angle BCD = 40 o and angle BDC is
right angle.
B
5 cm
40
o
D
C
i.
Calculate the length , in m, of BD
Ans:
Sin
=
Sin40 =
BD = 5 sin 40
BD = 3.213
In meters BD =
= 0..321m
ii.
Calculate the length, in m, of DC
Ans:
Cos
Cos 40 =
DC = 5 cos 40
DC = 3.83cm
In meters DC =
= 0.0383
iii.
Prove that the area in m2, of the triangle BDC is 12.5sin40 ocos40o.
Ans:
= x BD x DC
( 5 sin 40) ( 5cos 40 )
sin 40 cos 40
4. The points X, Q and R are on a straight line in the same horizontal plane. The angle
of depression of a point Q from the top of a tower PX, 10 m high is 70 o. The angle of
depression of R from the top of the tower is 40 o. Calculate the distance QR to one
decimal place.
Ans:
First by triangle XPQ
∠XPQ = 30˚
PX = 10m
XQ = PX tan
= 10 tan 30˚
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Unit 13
Trigonometry
5.77m
Now by triangle XPR
∠XPR = 60˚
PX = 10m
XR = PX tan
= 10 tan 60˚
XR = 17.32m
Now distance from Q to R
QR = XP – XQ
= 17.32 – 5.77
= 11.55m
5. A plane takes off at an angle of elevation of 17o to the ground. After 25 seconds the
plane has travelled a horizontal distance of 2400 metres.
i.
Draw a sketch to represent the given information.
ii.
Calculate to 2 significant figures the height of the plane above the ground
after 25 seconds.
Ans: OD = 2400m
∠POQ = 17˚
PQ = OQ tan
= 2400 tan 17˚
= 733.75m
Height of plane = 733.75m
6. Three towns, P, Q, and R are such that the bearing of P from Q is 070 o. R is 10 km due
east of Q and PQ = 5 km.
i.
Calculate, correct to one decimal place, the distance PR.
PR = 14.8 km.
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Unit 13
Trigonometry
ii.
Given that angle QPR = 142 o, what is the bearing of R from P?
W6.64oS or 263.36o
7. A ship leaves a point C, and travels on a bearing of 037 o to a point, D, 12 km from C.
The ship changes its course and travels 25 km on a bearing of 140 o to a point E.
i.
Draw a sketch of the ships journey, marking clearly
a. The North direction
b. The bearings 037o and 140o.
c. The points C, D and E
ii.
iii.
Calculate, the distance, in km, of CE to 2 decimal places,
CE = 25.18 km
Determine the bearing of E from C
27.67o
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