Triangular Field Calculations

00:00 6 marks

The diagram shows a triangular field ABC. AB = 65 m, AC = 80 m, and angle BAC = 55°.

(a) Calculate the length of BC. [3]
(b) Calculate the area of the field ABC. [2]
(c) Calculate the angle ABC. [1]

Part a

3 minutes 3 marks

Question

Calculate the length of BC. [3]

Hint Hint

Hint

Apply the cosine rule: \(BC^2 = 65^2 + 80^2 – 2 \times 65 \times 80 \times \cos(55°)\).

Answer Answer
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Complete Answer

\(BC \approx 68.3\) m

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Part b

3 minutes 2 marks

Question

Calculate the area of the field ABC. [2]

Hint Hint

Hint

Use the formula: \(\text{Area} = \frac{1}{2} \times AB \times AC \times \sin(55°)\).

Answer Answer
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Complete Answer

\(\text{Area} \approx 2130\) m²

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Part c

2 minutes 1 marks

Question

Calculate the angle ABC. [1]

Hint Hint

Hint

Apply the sine rule: \(\frac{\sin(ABC)}{AC} = \frac{\sin(55°)}{BC}\) and solve for \(\angle ABC\).

Answer Answer
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Complete Answer

\(\angle ABC \approx 73.7°\)

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