**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 30^{0} 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 30^{0} 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.

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