Problem 1: A ship leaves a port P and travel 30 km due north. Then it changes course and travels 20 km in a direction 30⁰ east of north to reach port R. Calculate the distance from P to R.

Solution

Given Distance 1 = 30 km due north

Distance 2 = 20 km at 30⁰ east of north

Required Displacement between P and R

Details Draw the sketch as below.

P is the point from where the ship takes the start. If Q is the point from where the ship takes the turn to right, then according to the chosen scale

PQ = 1.5 cm,    QR = 1 cm.

Measure PR which is about 2.4 cm. Convert to kilometers according to the chosen scale;

2.4 * 20 = 48.4 km

This is the distance between the two ports.