Attempt to find gradient of the ladder (M1)
EITHER: Gradient of tangent = \( -\tan 75^\circ \approx -3.73205 \) or \( -2 – \sqrt{3} \)
OR: Gradient of tangent = \( \tan 105^\circ \approx -3.73205 \) (A1)
Derivative of curve: \( y = 5 \cos(1.1x) \), \( \frac{dy}{dx} = -5.5 \sin(1.1x) \) (A1)
Equate derivative to gradient: \( -5.5 \sin(1.1x) = -3.73205 \)
Solve: \( \sin(1.1x) = \frac{3.73205}{5.5} \approx 0.67855 \), \( x \approx 0.677993 \) (A1)
Substitute into curve equation: \( \text{height} = 5 \cos(1.1 \times 0.677993) \) (M1)
Calculate: \( \text{height} \approx 5 \cos(0.745792) \approx 3.67274 \)
Round to 3 significant figures: 3.67 m (A1)
Result: 3.67 m [5]