QuestionQuestion 8 (2 marks)
From the top of a cliff 67 metres above sea level, the angle of depression of a buoy is $38^{\circ}$. How far 2 is the buoy from the base of the cliff to the nearest metre?

Studdy Solution
Calculate the horizontal distance using the tangent function:
- Rearrange the tangent equation to solve for the horizontal distance:
$$\text{Horizontal distance} = \frac{\text{Height of the cliff}}{\tan(38^\circ)}$$
- Substitute the given values:
$$\text{Horizontal distance} = \frac{67}{\tan(38^\circ)}$$
- Calculate the value using a calculator:
$$\text{Horizontal distance} \approx \frac{67}{0.7813} \approx 85.75$$
- Round to the nearest metre:
$$\text{Horizontal distance} \approx 86 \text{ metres}$$
The buoy is approximately:
$$\boxed{86 \text{ metres}}$$