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A triangular plot of land has two sides measuring 20 m and 25 m, with an angle of 48 degrees between them. Part a) Calculate the area of the plot. Part b) If the third side measures 18.5 m, calculate

Mathematics

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3 parts
a

185.79 m2\text{185.79 m}^2

b

63.5 m\text{63.5 m}

c

K2857.50\text{K2857.50}

Step-by-step solution

7 steps

Part a· 3 steps

  1. Identify the given values for the area formula.

    The two sides are a=20a = 20 m and b=25b = 25 m. The angle between them is C=48∘C = 48^\circ.

  2. Substitute the values into the area formula and calculate.

    Area=12×a×b×sin⁡C\text{Area} = \frac{1}{2} \times a \times b \times \sin C Area=12×20 m×25 m×sin⁡48∘\text{Area} = \frac{1}{2} \times 20 \text{ m} \times 25 \text{ m} \times \sin 48^\circ Area=10 m×25 m×0.7431448...\text{Area} = 10 \text{ m} \times 25 \text{ m} \times 0.7431448... Area=250 m2×0.7431448...\text{Area} = 250 \text{ m}^2 \times 0.7431448... Area=185.7862... m2\text{Area} = 185.7862... \text{ m}^2

  3. Round the area to 2 decimal places.

    Area=185.79 m2\text{Area} = 185.79 \text{ m}^2

    The area of the plot is 185.79 m2\boxed{\text{185.79 m}^2}.

Part b

63.5 m\text{63.5 m}

  1. Identify the lengths of all three sides.

    The two given sides are 20 m and 25 m. The third side is 18.5 m.

  2. Calculate the total length of fencing required (perimeter).

    Perimeter=Side 1+Side 2+Side 3\text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} Perimeter=20 m+25 m+18.5 m\text{Perimeter} = 20 \text{ m} + 25 \text{ m} + 18.5 \text{ m} Perimeter=63.5 m\text{Perimeter} = 63.5 \text{ m}

    The total length of fencing required is 63.5 m\boxed{\text{63.5 m}}.

Part c

K2857.50\text{K2857.50}

  1. Use the perimeter from part (b) and the cost per metre.

    The total length of fencing is 63.5 m. The cost per metre is K45.00.

  2. Calculate the total cost of fencing.

    Total Cost=Perimeter×Cost per metre\text{Total Cost} = \text{Perimeter} \times \text{Cost per metre} Total Cost=63.5 m×K45.00/m\text{Total Cost} = 63.5 \text{ m} \times \text{K}45.00/\text{m} Total Cost=K2857.50\text{Total Cost} = \text{K}2857.50

    The total cost of fencing this plot is K2857.50\boxed{\text{K2857.50}}.

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