Question
Download Solution PDFA vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively. What is the height of the tower ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A flagstaff of height h is surmounted on a verticle tower.
Angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively.
Formula used:
1. tan θ = Perpendicular/Base
2. tan 2θ =
3. cos 2θ =
Calculation:
Let the height of the tower be x.
In right triangle ABC
tan θ = AC/AB = x/AB
⇒ AB = x/tan θ ------(1)
In right triangle ABD
tan 2θ = AD/AB = (x + h)/AB
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒ x = hcos 2θ
∴ The height of the tower is h cos 2θ
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