Mathematical Methods Β· Unit 4 Β· Trigonometry Β· Cosine and sine rules
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A triangular piece of land has two adjacent sides measuring \(85\) m and \(120\) m, with an included angle of \(68^\circ\). (a) Use the cosine rule to determine the length of the third side of the triangle, correct to one decimal place. (2 marks) (b) Use your answer from part (a) to determine the area of the triangular piece of land, correct to the nearest square metre. (2 marks)
Determine the length of side c in the triangle.
A surveyor is measuring the distance across a lake. From point A, she measures the distance to point B as 450 m and the distance to point C as 620 m. The angle at A between the lines AB and AC is 72Β°. Determine the distance BC across the lake, correct to the nearest metre.
A triangular parcel of land has two adjacent sides of length 85 m and 112 m. The angle between these two sides is 73Β°. (a) Use the cosine rule to determine the length of the third side of the parcel, correct to the nearest metre. (b) Use the information from part (a) to determine the size of the smallest angle in the triangle, correct to the nearest degree.