1 of 8 0-day streak

Solve a practical triangle problem end to end

Question 1 of 8

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The following measurements describe the patrol route

The route starts at \(R\), reaches \(S\) after 53 km on a true bearing of 070° (70° east of north), and then reaches \(T\) after 53 km on a true bearing of 154° (26° east of south). Bearings are measured clockwise from the north ray at the point where each leg begins

At \(S\), the return ray \(SR\) has bearing 250°. The angle between \(SR\) and \(ST\) is therefore \(96^{\circ}\). The direct closing side \(TR\) is unknown. The return speed along \(TR\) is 30 km/h

(a)1 mark

Which rule should be used for 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 Pythagoras because two perpendicular side lengths determine the first diagonal

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

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

(b)1 mark

Calculate the direct return distance to 1 decimal place

Direct return distance (km) Format: 1 d.p.

Complete the second stage and give the direct return time to 1 decimal place

Direct return time (min) Format: 1 d.p.