 Given sin (90 – a) = ½ , find without using trigonometric tables the value of cos a (2mks)
 If tan θ = 25/45 ,find without using tables or calculator, the value of
(tan θ – cos θ)/ (cos θ + sin θ)
(3 marks)
 At point A, David observed the top of a tall building at an angle of 30^{o}. After walking for
100meters towards the foot of the building he stopped at point B where he observed it again
at an angle of 60^{o}. Find the height of the building
 Find the value of q, given that ½ sin q = 0.35 for 0^{o} ≤ θ ≤ 360^{o}
 A man walks from point A towards the foot of a tall building 240 m away. After covering
180m, he observes that the angle of elevation of the top of the building is 45^{o}. Determine
the angle of elevation of the top of the building from A
 The table below gives a field book showing the results of a survey of a section of a piece of land
between A and E. All measurements are in metres.
D33
C21 B 42

E
95 90 70 30 25 A 
F 36
G 25 H 40 
(a) Draw a sketch of the land.
(b) Calculate the area of this piece of land.
 Solve for x in 2 Cos2x^{0 }= 0.6000 0^{0}≤ x ≤ 360^{0}.
 Wangechi whose eye level is 182cm tall observed the angle of elevation to the top of
her house to be 32º from her eye level at point A. she walks 20m towards the house
on a straight line to a point B at which point she observes the angle of elevation to the
top of the building to the 40º. Calculate, correct to 2 decimal places the ;
a)distance of A from the house
 b) The height of the house
 Given that cos A = ^{5}/_{13} and angle A is acute, find the value of:
2 tan A + 3 sin A
 Given that tan 5° = 3 + 5, without using tables or a calculator, determine tan 25°, leaving
your answer in the form a + b √c
 A student whose eye level is 182cm from the ground observed the top of their house at
an angle of elevation of 32^{o} at point A. She walked for 20m towards the house along a
the straight road to a point B, where she observed the top of the building again at an angle of
elevation of 40^{o}. Calculate correct to 2 decimal places the:
(a) Distance of A from the house
(b) The height of the house
 Given that tan x = 5, find the value of the following without using mathematical tables or
calculator: 12
(a) Cos x
(b) Sin^{2}(90x)
 If tan θ =^{8}/_{15}, find the value of Sinθ – Cosθ without using a calculator or table
Cosθ + Sinθ
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