Question 1

Paper 1Medium6 marks

A mapping team approximates a wetland by triangle ABCABC The horizontal distance between survey stations AA and BB is 1.80 km1.80\text{ km} The measured interior angles are ∠BAC=52.6∘\angle BAC=52.6^\circ and ∠ABC=68.3∘\angle ABC=68.3^\circ

The wetland qualifies for a reserve if its mapped area is at least 1.20 km21.20\text{ km}^2

(a)

Find ∠ACB\angle ACB

[1]
(b)

Show that AC=1.95 kmAC=1.95\text{ km} correct to three significant figures.

[2]
(c)

Hence, using your answer to part (b), calculate the area of triangle ABCABC correct to three significant figures, and state whether the wetland qualifies for a reserve.

[3]

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