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 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
2. Find the value of θ, given that ½ sinθ = 0.35 for 0^º ≤ θ ≤ 360^º
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 45^º. 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 2Cos2x^º=0.6000 0^º≤x≤ 360^º
6. Wangechi whose eye level is 182cm tall observed the angle of elevation to the top of her house to be 32^º 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 40^º. 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

Answers

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 √
   = 5,147.5m^²
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
7. 
   
   1. cos x = ¹²/₁₃
   2. Sin2990-x)
      = (¹²/₁₃)^²= ¹⁴⁴/₁₆₉
8. Tan θ = ⁸/₁₅ C
   
   AB^² = 8^² + 15^²
   AB = √289 = 17
   Sin θ = ⁸/₁₇, cos θ = ¹⁵/₁₇