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The diagram shows the positions of two towns, Amton and Bisham - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Question 9

The diagram shows the positions of two towns, Amton and Bisham. The bearing of Bisham from Amton is $b^\circ$. The bearing of Amton from Bisham is $6b^\circ$. Calc... show full transcript

Worked Solution & Example Answer:The diagram shows the positions of two towns, Amton and Bisham - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Step 1

Step 1: Establish the Relationship Between Bearings

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Answer

Given that the bearing of Bisham from Amton is $b^\circ$ , the bearing of Amton from Bisham can be expressed as:

$b + 180^\circ$

This is because bearings that are 180 degrees apart are directly opposite on a circle.

Step 2

Step 2: Set Up the Equation

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Answer

From the information provided, we know that:

$6b = b + 180$

This can be rearranged to:

$6b - b = 180$

Step 3

Step 3: Solve for b

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Solving the equation gives:

$5b = 180$

Thus:

$b = \frac{180}{5}$

$b = 36^\circ$

Step 4

Step 4: Calculate the 3-Figure Bearing of Amton from Bisham

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Now, substituting $b$ back into the relationship derived in Step 1:

$\text{Bearing of Amton from Bisham} = 6b = 6 \times 36 = 216^\circ$

Therefore, the 3-figure bearing of Amton from Bisham is $216^\circ$ .

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The diagram shows the positions of two towns, Amton and Bisham - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Worked Solution & Example Answer:The diagram shows the positions of two towns, Amton and Bisham - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

Step 1: Establish the Relationship Between Bearings

Step 2: Set Up the Equation

Step 3: Solve for b

Step 4: Calculate the 3-Figure Bearing of Amton from Bisham

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