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Some Applications of Trigonometry
CBSE 2026 Board Exam Set 1 (Code 30/1/1)
CBSE_BOARD_PYQ_2026_30_1_1
Grade 10
Question:
[Section E]
Case Study 3: Lighthouse Observation
A lighthouse is a tower with a bright light at the top to guide ships at sea. From the top of a $75$ m high lighthouse from the sea level, the angles of depression of two ships approaching it from the same side are observed to be $30^\circ$ and $45^\circ$.
1. Draw a neat labelled mathematical diagram representing the scenario. (1 Mark)
2. Find the distance of the nearer ship from the foot of the lighthouse. (1 Mark)
3. Find the distance between the two ships. (Use $\sqrt{3} \approx 1.732$). (2 Marks)
Case Study 3: Lighthouse Observation
A lighthouse is a tower with a bright light at the top to guide ships at sea. From the top of a $75$ m high lighthouse from the sea level, the angles of depression of two ships approaching it from the same side are observed to be $30^\circ$ and $45^\circ$.
1. Draw a neat labelled mathematical diagram representing the scenario. (1 Mark)
2. Find the distance of the nearer ship from the foot of the lighthouse. (1 Mark)
3. Find the distance between the two ships. (Use $\sqrt{3} \approx 1.732$). (2 Marks)
Step-by-Step Solution
Key Concept: Right triangles with height 75 m.
1. Diagram representation. [1.0 Mark]
2. Distance of nearer ship $= 75$ m. [1.0 Mark]
3. Distance between ships $= 75(\sqrt{3} - 1) = 75(0.732) = 54.9$ m. [2.0 Marks]
2. Distance of nearer ship $= 75$ m. [1.0 Mark]
3. Distance between ships $= 75(\sqrt{3} - 1) = 75(0.732) = 54.9$ m. [2.0 Marks]
Correct Answer: 1. Diagram, 2. 75 m, 3. 54.9 m
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