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Homefsc 1st year math solutionsSolution of Triangle with law of cosine Exercise 12.7

Solution of Triangle with law of cosine Exercise 12.7

  1. Find the area of the triangle A B C, given two sides and their included angle:
    i) a=200, b=120
    ii) b=37, c=45 \quad, \alpha=30^{\circ} 50^{\circ}
    iii) a=4.33 \quad, b=9.25 \quad, \gamma=56^{\circ} 44^{\prime}
  2. Find the area of the triangle A B C, given one side and two angles:
    i) b=25.4, \gamma=36^{\circ} 41^{\circ}, \alpha=45^{\circ} 17^{\circ}
    ii) c=32, \alpha=47^{\circ} 24^{,}, \beta=70^{\circ} 16^{\circ}
    iii) a=4.8, \alpha=83^{\circ} 42^{\circ}, \gamma=37^{\circ} 12^{\prime}
  3. Find the area of the triangle A B C, given three sides:
    i) a=18 b=24 \quad, c=30
    ii) a=524 \quad, b=276 \quad, c=315
    ii) a=32.65, b=42.81, \quad c=64.92
  4. The area of triangle is 2437 . If a=79, and c=97, then find angle \beta,
  5. The area of triangle is 121.34. If \alpha=32^{\circ} 15, \beta=65^{\circ} 37 then find c and angle \gamma.
  6. One side of a triangular garden is 30 \mathrm{~m}. If its two corner angles are 22^{\circ} \frac{1}{ 2} and 112^{\circ} \frac{1}{ 2}, find the cost of planting the grass at the rate of Rs. 5 per square meter.
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