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Measurement, STD1 2026 HSC 16

From the top of a cliff 439 m above sea level, the angle of depression to a dolphin is 30°.
 

  1. Label the diagram with the given information.   (2 marks)

  2. How far is the dolphin from the base of the cliff? Give your answer to the nearest metre.   (2 marks)

  3. The dolphin is swimming at a speed of 140 m/min.
  4. The dolphin swims directly towards the base of the cliff.
  5. How far from the base of the cliff is the dolphin after 2 minutes, correct to the nearest metre?   (2 marks)

Show Answers Only

a.    \(\text{See Worked Solution}\)

b.    \(760\ \text{m}\)

c.    \(480\ \text{m}\)

Show Worked Solution

a.    \(\text{Labelled diagram:}\)


 

b.    \(\text{Let}\ d=\text{distance of dolphin from base of cliff}\)

\(\tan 30^{\circ}\) \(=\dfrac{439}{d}\)
\(d\) \(=\dfrac{439}{\tan 30^{\circ}}=760.37…=760\ \text{m (nearest metre)}\)

 

c.    \(\text{Distance swum in 2 minutes}=140\times 2=280\ \text{m}\)

\(\text{Distance from base}\) \(=760.37…-280\)
  \(=480.37…\)
  \(=480\ \text{m (nearest metre)}\)