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A, B, C and D are four towns - OCR - GCSE Maths - Question 7 - 2017 - Paper 1
Question 7
A, B, C and D are four towns. B is 25 kilometres due East of A. C is 25 kilometres due North of A. D is 45 kilometres due South of A. (a) Work out the bearing of B ... show full transcript
Worked Solution & Example Answer:A, B, C and D are four towns - OCR - GCSE Maths - Question 7 - 2017 - Paper 1
Step 1
Work out the bearing of B from C.
Answer
To find the bearing of B from C, we first need to determine the position of A relative to C and B.
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Positioning:
- A is the reference point at (0, 0).
- B is at (25, 0).
- C is at (0, 25).
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Finding Coordinates:
- C to A: moves 25 km South to reach point A.
- B is 25 km East of A.
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Calculating the angle:
- Draw a line from C to B.
- The angle at point A formed by the North (vertical line) and line CB can be found using the tangent function:
- Thus, ( \theta = 45^{\circ} ).
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Finding the Bearing:
- Bearings are measured clockwise from North. Therefore, the bearing of B from C is:
Step 2
Calculate the bearing of D from B.
Answer
To determine the bearing of D from B, we need to establish the coordinates of D:
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Positioning:
- D is 45 km South of A, making its coordinates (0, -45).
- B is at (25, 0).
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Drawing a Triangle:
- From B, draw a line to D.
- You will create a right triangle, with A as a common point.
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Calculating the Angle at A:
- The angle at A (angle DAB) can be found using the tangent function:
- The vertical distance from A to D is 45 km, and from A to B is 25 km.
- The angle can be found using:
- The angle at A (angle DAB) can be found using the tangent function:
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Calculating the Bearing:
- Calculate ( \phi ) and add it to the 270° bearing from North (South direction):
- This gives us a bearing of approximately 209° to 209.1°.