1 of 8 0-day streak

Solve a practical triangle problem end to end

Question 1 of 8

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A marine research vessel uses the following measurements for the sampling route

The route starts at \(V\), reaches \(W\) after 130 km on a true bearing of 045° (45° east of north), and then reaches \(X\) after 130 km on a true bearing of 099° (81° east of south). Bearings are measured clockwise from the north ray at the point where each leg begins

At \(W\), the return ray \(WV\) has bearing 225°. The angle between \(WV\) and \(WX\) is therefore \(126^{\circ}\). The direct closing side \(XV\) is unknown. The return speed along \(XV\) is 15 km/h

(a)1 mark

Which rule should be used for the first unknown?

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

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

(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.