Apply trigonometric methods in solving problems.
Introduction: Awaroa Inlet is a tidal estuary in the Abel Tasman National Park. The inlet is on a popular walking
track and can only be crossed at certain times of the day because of the tides. When the tide comes in and the
water passes a certain depth it is not safe for walkers to cross the Inlet. It usually takes about 30 minutes to
cross the inlet. Information on the tides is provided in resource 2.
Task:
1.
a.Find a model for the depth of the water at Awaroa Inlet.
b. Find the period of time when it is safe to cross the inlet.
- Tides vary so the high tide and low tide height of the water is different every day. At certain times of the year,
such as a Spring tide, the water can be very deep and it may not be safe to cross the inlet. During one big tide
the water was 3.9 metres deep at high tide and 0.7 metres deep at low tide.
The Department of Conservation (DOC) recommends that walkers only cross the inlet within one and a half
hours before low tide and two hours after low tide.
Find a safe time to cross the inlet during this big tide and discuss DOC’s recommendation in relation to your
findings for both tidal situations.
Explain what you are calculating clearly and also state what you have found at the end of the calculation. Link
your reasoning's to the context.
Sample Solution