1 of 8 0-day streak

Solve a practical triangle problem end to end

Question 1 of 8

Calculator allowed

A coastal survey vessel records measurements for the survey route

The route starts at \(M\), reaches \(N\) after 21 km on a true bearing of 052° (52° east of north), and then reaches \(P\) after 21 km on a true bearing of 100° (80° east of south). Bearings are measured clockwise from the north ray at the point where each leg begins

At \(N\), the return ray \(NM\) has bearing 232°. The angle between \(NM\) and \(NP\) is therefore \(132^{\circ}\). The direct closing side \(PM\) is unknown. The return speed along \(PM\) is 11 km/h

(a)1 mark

Select the rule supported by the first triangle's given data

Use Pythagoras because two perpendicular side lengths determine the first diagonal

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

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

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

(b)1 mark

Find the first required length, giving 1 decimal place

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

Carry full precision into the next calculation. Determine the direct return time to 1 decimal place

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