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The accurate scale drawing shows the positions of port P and a lighthouse L - Edexcel - GCSE Maths - Question 9 - 2019 - Paper 1
Question 9
The accurate scale drawing shows the positions of port P and a lighthouse L. Scale: 1 cm represents 4 km. Aleena sails her boat from port P on a bearing of 070°. S... show full transcript
Worked Solution & Example Answer:The accurate scale drawing shows the positions of port P and a lighthouse L - Edexcel - GCSE Maths - Question 9 - 2019 - Paper 1
Step 1
the distance, in km, of port Q from lighthouse L
Answer
To find the distance from port P to port Q, we first calculate the distance Aleena sails.
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Calculate the distance traveled:
Distance = Speed × Time
Here, Speed = 12 km/h and Time = 1.5 hours.
So, Distance PQ = 12 × 1.5 = 18 km.
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Use the scale to find position of Q:
Since the drawing shows that 1 cm represents 4 km, we must first find the length of PQ on the drawing:
Length on drawing = Distance / Scale factor = 18 km / 4 km/cm = 4.5 cm.
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Finding distance from lighthouse L:
Using Pythagoras's theorem, if we let D be the distance from point P to L, we can calculate using the positions from the diagram:
Distance from L to Q can be calculated as follows, considering the angles. However, for the exact value, you would need the specific coordinates from the diagram.
Step 2
the bearing of port Q from lighthouse L
Answer
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Understanding Bearings:
A bearing is measured from the North in a clockwise direction. Since Aleena sails on a bearing of 070°, we will need to calculate the angle added to find the angle with respect to lighthouse L.
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Calculate the Bearing:
Since port P is directly south of lighthouse L (from the diagram), the bearing of Q from L can be represented as:
Bearing of Q from L = 090° + 070° = 160°.
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Final Answer:
Thus, the bearing of port Q from lighthouse L is 160°.