ICSE Class X Math 2013 Solved Paper

In the figure given, from the top of a building AB=60m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30∘ and 60∘ respectively. Find :

Question : 31

Total: 46

The height of the lamp post.

Solution:

Let AE=x and proved above BC=20 √3m
∴‌‌BC=ED=20√3
Now in △ AED,
tan‌30∘‌=‌

⇒‌‌

√3

‌=‌

20√3

⇒√3‌AE‌=20√3
‌ now ‌‌AE‌=20m
∴‌EB‌=AB−AE
∵‌EB‌=60−20=40m
∴‌EB‌=CD
‌CD‌=40m
Hence, the height of the lamp post = 40m .

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