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ICSE Class 10 Mathematics Question 11 of 21

Solved 2024 Question Paper ICSE Class 10 Mathematics — Question 5

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5
Question

Question 5(ii)

The angle of elevation of the top of a 100 m high tree from two points A and B on the opposite side of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre.

The angle of elevation of the top of a 100 m high tree from two points A and B on the opposite side of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre. ICSE 2024 Maths Solved Question Paper.
Answer

From figure,

⇒ tan 52° = CDAC\dfrac{CD}{AC}

⇒ 1.28 = 100AC\dfrac{100}{AC}

⇒ AC = 1001.28\dfrac{100}{1.28} = 78.125 m

⇒ tan 45° = CDBC\dfrac{CD}{BC}

⇒ 1 = 100BC\dfrac{100}{BC}

⇒ BC = 100 m

⇒ AB = AC + BC = 78.125 + 100 = 178.125 m

Hence, AB = 178.125 m