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ICSE Class 10 Mathematics Question 19 of 21

Solved 2023 Question Paper ICSE Class 10 Mathematics — Question 18

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Question 9(iii)

From the top of a tower 100 m high, a man observes the angle of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of tower and the ships are in the same horizontal line, find the distance between two ships A and B to the nearest metre.

From the top of a tower 100 m high, a man observes the angle of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of tower and the ships are in the same horizontal line, find the distance between two ships A and B to the nearest metre. ICSE 2023 Maths Solved Question Paper.
Answer

Let CD be the tower.

From the top of a tower 100 m high, a man observes the angle of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of tower and the ships are in the same horizontal line, find the distance between two ships A and B to the nearest metre. ICSE 2023 Maths Solved Question Paper.

From figure,

⇒ ∠A = ∠EDA = 45° (Alternate angles are equal)

⇒ ∠B = ∠FDB = 38° (Alternate angles are equal)

In △ ACD,

⇒ tan A = CDAC\dfrac{CD}{AC}

⇒ tan 45° = 100AC\dfrac{100}{AC}

⇒ AC = 100tan 45°=1001\dfrac{100}{\text{tan 45°}} = \dfrac{100}{1} = 100 m.

In △ BCD,

⇒ tan B = CDBC\dfrac{CD}{BC}

⇒ tan 38° = 100BC\dfrac{100}{BC}

⇒ BC = 100tan 38°=1000.7813\dfrac{100}{\text{tan 38°}} = \dfrac{100}{0.7813} = 127.99 m.

From figure,

The distance between ships A and B = AC + BC

= 100 + 127.99

= 227.99 m ≈ 228 m.

Hence, the distance between the two ships A and B = 228 m.