Mathematics 10 — Exercise 7.3 · Q11

Full question

A lighthouse is on an 80 m cliff. A ship is seen at 12° depression. Find the horizontal distance from the cliff base.

Step-by-step solution

1. Tangent is height/horizontal distance. Divide the known height by the tangent.

2. Substitute the given values into the displayed formula.

   $$\mathrm{required\; length}=\frac{80}{\tan \left(\mathrm{12°}\right)}$$

3. Evaluate the powers and trigonometric values before the final arithmetic.

   $$\mathrm{required\; length}=376.37041$$

4. Round only the final result, keeping full precision for later calculations.

   $$\mathrm{required\; length}=\mathrm{376.370}$$

Answer

The final answer is shown below.