Exam Questions & Step-by-Step Markschemes (3 Problems)
Question 1 • 2023
5 Marks
From the top of a cliff 150\text{ m} high, the angles of depression of two ships anchored in the sea in the same vertical plane and on the same side of the cliff are observed to be 30^\circ and 45^\circ respectively. Find the distance between the two ships (take \sqrt{3} \approx 1.732 ).
Answer: \text{Distance between ships} = 109.8\text{ m}
Question 2 • 2022
3 Marks
Prove the trigonometric identity: \frac{\sin\theta}{1 + \cos\theta} + \frac{1 + \cos\theta}{\sin\theta} = 2\csc\theta
Answer: \text{LHS} = \text{RHS} \quad (\text{Proved})
Question 3 • 2024
6 Marks
As observed from the top of a 80\text{ m} high lighthouse from the sea-level, the angles of depression of two ships are 30^\circ and 45^\circ . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Take \sqrt{3} = 1.732 )
Answer: CD = 58.56 \text{ m}