Triangular Field Measurements

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

4 minutes 3 marks

Question

Calculate the length of BC. [3]

Hint Hint

Hint

Apply the cosine rule: \(BC^2 = AB^2 + AC^2 – 2\cdot AB\cdot AC\cdot \cos(55°)\). Then take the square root.

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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 area formula for a triangle: \(Area = \frac{1}{2}\cdot AB\cdot AC\cdot \sin(55°)\).

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Complete Answer

\(Area \approx 2130\,m²\)

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Part c

3 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 then solve for angle ABC.

Answer Answer
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Complete Answer

\(\angle ABC \approx 73.7°\)

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