QCEVault

Trigonometry — Question 326

Original QCE Vault practice · 6 marks

Q326 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 326 (6 marks)

Two rigid arms of lengths 1010 m and 1414 m form two sides of a triangular projection. Their included angle is θ(t)=πt/12\theta(t)=\pi t/12 radians, where 0<t≤60<t\leq6 seconds.
Triangular projection with two sides 10 m and 14 m and included angle theta(t). Not to scale.
a)
Write the area A(t)A(t) and its rate of change.
[2 marks]
b)
Determine the interval when the area is at least 56 m256\ \mathrm{m}^2 and is increasing at more than 8 m28\ \mathrm{m}^2/s. Give endpoints to 0.010.01 s and indicate which endpoints are included.
[4 marks]
Question linkSyllabus coverage

Related questions

  1. Q7 · Original practice · 1 mark
    In triangle ABCABC, AB=10AB=10, AC=7AC=7 and ∠A=60∘\angle A=60^\circ. Determine BCBC.
    Trigonometry
  2. Q17 · Original practice · 1 mark
    In a triangle, side a=5a=5 is opposite A=30∘A=30^\circ. Side bb is opposite B=45∘B=45^\circ. Determine bb.
    Trigonometry
  3. Q32 · Original practice · 2 marks
    Triangle ABCABC has AB=11AB=11, AC=8AC=8 and ∠A=30∘\angle A=30^\circ. Determine its area.
    Trigonometry
  4. Q42 · Original practice · 5 marks
    In triangle ABCABC, AB=120AB=120 m, AC=80AC=80 m and ∠A=70∘\angle A=70^\circ. Determine BCBC and ∠B\angle B to one decimal place.
    Trigonometry