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ICSE Class 10 Mathematics Question 15 of 21

Solved 2024 Specimen Paper ICSE Class 10 Mathematics — Question 11

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11
Question

Question 7(ii)

The angles of depression of two ships A and B on opposite sides of a light house of height 100 m are respectively 42° and 54°. The line joining the two ships passes through the foot of the light house.

(a) Find the distance between the two ships A and B.

(b) Give your final answer correct to the nearest whole number.

(Use mathematical tables for this question)

The angles of depression of two ships A and B on opposite sides of a light house of height 100 m are respectively 42° and 54°. The line joining the two ships passes through the foot of the light house. ICSE 2024 Maths Specimen Solved Question Paper.
Answer

Let ∠BCP = α and ∠ACP = β

The angles of depression of two ships A and B on opposite sides of a light house of height 100 m are respectively 42° and 54°. The line joining the two ships passes through the foot of the light house. ICSE 2024 Maths Specimen Solved Question Paper.

From figure,

⇒ α + 54° = 90°

⇒ α = 90° - 54° = 36°.

⇒ β + 42° = 90°

⇒ β = 90° - 42° = 48°.

⇒ tan α = BPCP\dfrac{BP}{CP}

⇒ tan 36° = BP100\dfrac{BP}{100}

⇒ 0.7265 = BP100\dfrac{BP}{100}

⇒ BP = 0.7265 × 100 = 72.65 m

⇒ tan β = APCP\dfrac{AP}{CP}

⇒ tan 48° = AP100\dfrac{AP}{100}

⇒ 1.1106 = AP100\dfrac{AP}{100}

⇒ AP = 1.1106 × 100 = 111.06 m

(a) From figure,

AB = AP + BP = 72.65 + 111.06 = 183.71 m

Hence, the distance between two ships = 183.71 m.

(b) On rounding off,

AB = 184 m.

Hence, the distance between two ships = 184 m.