A sailor on a boat 380 metres from the base of a cliff sights the top of a lighthouse on the cliff. The angle of elevation from the ocean to the top of the lighthouse is $28.6^{\circ}$.
a) Draw a neat diagram to display this information.
b) Calculate the height of the top of the lighthouse above the ocean.
Answer
\(\boxed{\text{The height of the top of the lighthouse above the ocean is approximately 207.18 meters}}\)
Step 1 ：Draw a neat diagram to display this information.
Step 2 ：Use the tangent function to solve the problem: \(\tan(\theta) = \frac{height}{distance}\)
Step 3 ：Plug in the given values: \(\tan(28.6^\circ) = \frac{height}{380}\)
Step 4 ：Solve for height: \(height = 380 \times \tan(28.6^\circ)\)
Step 5 ：Calculate the height: \(height \approx 207.18\)
Step 6 ：\(\boxed{\text{The height of the top of the lighthouse above the ocean is approximately 207.18 meters}}\)
