# Trigonometric Ratio

1. Given sin (90 – a) = ½ , find without using trigonometric tables the value of cos a (2mks)
2. If tan θ = 25/45  ,find without using tables or calculator, the value of

(tan θ – cos θ)/ (cos θ + sin θ)

(3 marks)

1. At point A, David observed the top of a tall building at an angle of 30o. After walking for

100meters towards the foot of the building he stopped at point B where he observed it again

at an angle of 60o. Find the height of the building

1. Find the value of q, given that ½ sin q = 0.35 for 0o ≤ θ ≤ 360o

1. 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 45o. Determine

the angle of elevation of the top of the building from A

1. 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.

1. Solve for x in 2 Cos2x0 = 0.6000 00≤ x ≤ 3600.

1. 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

1.        b) The height of the house
2. Given that cos A = 5/13 and angle A is acute, find the value of:-

2 tan A + 3 sin A

1. Given that tan 5° = 3 + 5,     without using tables or a calculator, determine tan 25°, leaving

1. A student whose eye level is 182cm from the ground observed the top of their house at

an angle of elevation of 32o 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 40o.   Calculate correct to 2 decimal places the:-

(a) Distance of A from the house

(b) The height of the house

1. Given that tan x = 5, find the value of the following without using mathematical tables or

calculator:            12

(a) Cos x

(b) Sin2(90-x)

1. If tan θ =8/15, find the value of Sinθ – Cosθ without using a calculator or table

Cosθ + Sinθ
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