Question 1
A triangular field has two adjacent sides of length 120 m and 85 m. The angle between these two sides is 38Β°. What is the area of the field, correct to the nearest square metre?
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Mathematical Methods Β· Unit 4 Β· Trigonometry Β· Cosine and sine rules
Use the formula area = 1 2 π π sin (π΄) to calculate the area of a triangle.
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Question 2
A triangular garden bed has two adjacent sides of length $8 \text{ m}$ and $6 \text{ m}$, with an included angle of $65Β°$. Calculate the area of the garden bed in square metres, correct to 1 decimal place.
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Question 3
A surveyor measures a triangular piece of land. Two adjacent sides of the triangle measure 8.5 m and 6.2 m, and the included angle between them is 58Β°. Calculate the area of the land in mΒ², giving your answer correct to 1 decimal place.
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More in Cosine and sine rules
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Use the cosine rule, π2 = π2 + π2 β 2ππ cos(πΆ).
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Use the sine rule (ambiguous case is required), π sin(π΄) = π sin(π΅) = π sin(πΆ), where π, π and π are the side lengths of the triangle and π΄, π΅ and πΆ are the corresponding opposite angles.