from the top of the building 60m high,the angels og depression of the top and bottom of a tower are observed to be 30° and 60°.Find the height of the tower?
Answers
Answer:
The height of the lamp is 45 meters.
Step-by-step explanation:
Let the line segment AB represents the height of the lamp ( where A is the top of the lamp ), ED represents the height of the building,
While C is any point on ED such that CA ║ DB and CA = DB
Thus, by the below diagram,
In triangle ECA,
tan 30^{\circ}=\frac{EC}{CA}tan30
∘
=
CA
EC
\frac{1}{\sqrt{3}}=\frac{EC}{CA}\implies CA =\sqrt{3} EC
3
1
=
CA
EC
⟹CA=
3
EC
Now, in triangle EDB,
tan 60^{\circ}=\frac{ED}{DB}=\frac{60}{CA}tan60
∘
=
DB
ED
=
CA
60
\implies \sqrt{3}CA = 60\implies CA = \frac{60}{\sqrt{3}}⟹
3
CA=60⟹CA=
3
60
Thus,
√3 EC = 60 / √3
⇒ 3 EC = 60 ⇒ EC = 20
Since, AB = CD = ED - EC = 60 - 20 = 40 meters,
Hence, the height of the lamp post is 40 meters.
Step-by-step explanation:
see the attached image
there is some rough work which I had colored white
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