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Trigonometry, SMB-039

Gerry flies his helicopter from a heliport on a bearing of S50°W for 75 km until he stops at Town P which is due west of Town Q.

If Town Q is due south of the heliport, find the distance between the heliport and Town Q in kilometres, correct to two decimal places.   (3 marks)

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\(48.21\ \text{km} \)

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\(\text{Let}\ \ x=\ \text{distance from heliport and Town Q}\)

\(\cos 50^{\circ}\) \(= \dfrac{x}{75} \)  
\(x\) \(= 75 \times \cos 50^{\circ}\)  
  \(= 48.209…\)  
  \(= 48.21\ \text{km} \)  

Trigonometry, SMB-038

Boat A leaves port on a bearing of 065° and sails for 22 km until it is due east of Boat B. 

If Boat B is due north of the port, find the distance between the port and Boat B in kilometres, correct to two decimal places.   (3 marks)

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\(9.30\ \text{km} \)

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\(\text{Let}\ \ x=\ \text{distance from port to Boat B}\)

\(\cos 65^{\circ}\) \(= \dfrac{x}{22} \)  
\(x\) \(= 22 \times \cos 65^{\circ}\)  
  \(= 9.2976…\)  
  \(= 9.30\ \text{km} \)  

Trigonometry, SMB-035 MC

Peter is standing 8 metres due west of Mary.

Bob is standing 8 metres due north of Mary.

Bob is facing north. He then turns anticlockwise so that he is facing Peter.

How many degrees does Bob turn through?

  1. `45^@`
  2. `60^@`
  3. `120^@`
  4. `135^@`
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 `D`

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`text(Degrees Bob turns through)`

`= 90 + 45`

`= 135^@`

`=>D`