1 of 8 0-day streak

Solve a practical triangle problem end to end

Question 1 of 8

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A habitat survey team uses the following measurements for the inaccessible observation point

Survey points \(D\) and \(E\) are 140 m apart on a straight baseline. The inaccessible point is \(F\). At \(D\), the angle from ray \(DE\) to sight line \(DF\) is \(53^{\circ}\). At \(E\), the angle from ray \(ED\) to sight line \(EF\) is \(56^{\circ}\)

The third angle is \(F=180^{\circ}-53^{\circ}-56^{\circ}=71^{\circ}\). Side \(DF\) and the area of triangle \(DEF\) are unknown

(a)1 mark

What is the correct first method for this chain?

Use the cosine rule because two sides and their included angle determine the first unknown

Use a right-triangle trigonometric ratio because a right angle and a side with its marked acute angle determine the first unknown

Use the sine rule because a known side–opposite-angle pair and another angle determine the first unknown

Use Pythagoras because two perpendicular side lengths determine the first diagonal

(b)1 mark

Determine the first sight line, correct to 1 decimal place

First sight line (m) Format: 1 d.p.

What is the surveyed area, correct to 1 decimal place?

Surveyed area (m²) Format: 1 d.p.