# The Trigonometric Ratio 1 Questions and Answers - Form 2 Topical Mathematics

## Questions

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
2. Find the value of θ, given that ½ sinθ = 0.35 for 0º ≤ θ ≤ 360º
3. A man walks from point A towards the foot of a tall building 240m 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
4. 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.
1. Draw a sketch of the land.
2. Calculate the area of this piece of land.
5. Solve for x in 2Cos2xº=0.6000 0º≤x≤ 360º
6. 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 ;
1. Distance of A from the house
2. The height of the house
7. Given that tan x = 5/12, find the value of the following without using mathematical tables or calculator:
1. Cos x
2. Sin2(90-x)
8. If tan θ =8/15, find the value of Sinθ - Cosθ/Cosθ + Sinθ without using a calculator or table
9. Given that cos A = 5/13 and angle A is acute, find the value of:-
2tanA + 3sinA
10. Given that tan 5° = 3 + 5, without using tables or a calculator, determine tan 25°, leaving your answer in the form a + b√c

1. Tan 30° = x/(100 +y) x
x = (100 + y) tan 30°
(100 + y) tan 30° = y tan 60°
Tan 60° = x/y = x = y tan 60°
(100 + y) 0.5774 = 1.1732y
57.74 = 1.155y
y = 57.74/1.155
y = 49.99 ≡ 50m
∴ x = 50 tan 60
x = 86.6m
2. Sin θ= 0.70
θ= 44.43°, 135.57°

3. Tan 45 = AB/60
AB = 45
Tan θ = 45/240
= 0. 1875
θ = 10.62°

4. Area A: ½ x 25 (33 + 21) = 675
Area B: ½ x 40 (21 x 42) = 1260
Area C: ½ x 30 x 42 = 630
Area D: ½ x 25 x 40 = 500
Area E: ½ x 5 (40 + 25) = 162.5
Area F: ½ X 60 (25 + 36) = 1830
Area G: ½ x 5 x 36 = 90 √
= 5,147.5m²
5. 2Cos 2x = 0.600
Cos 2x = 0.3000
2x = 72.5o, 287.5
x = 36.250, 143.75
6.

1. Tan32° = h/(20 + x)
h = (20+x) tan32° = 12.498 + 0.6249x
tan 40° = h/x
h = x tan 40° = 0.8391x
0.8391x = 12.498 + 0.6249x
0.8391x – 0.6249x = 12.498
0.2142x = 12.498
x = 12.498/0.2142 = 58.35m

∴The distance of A from the house
= (20 + 58.35)m = 78.35
2. h = x tan 40°= 58.35 x 0.8391 = 48.96m
∴ The total height of the house
= 1.82m + 48.96m = 50.78m

1. cos x = 12/13
2. Sin2990-x)
= (12/13)²= 144/169
7. Tan θ = 8/15 C

AB² = 8² + 15²
AB = √289 = 17
Sin θ = 8/17, cos θ = 15/17

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