SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 93 of 100

Marks: +1, -0

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of the bottom of the flag staff is

α

and that of the top of the flag staff is

β

. Then the height of the tower is

h tan $\α$
${h \tan \α}/{\tan \β-\tan \α}$
${h \tan \α}/{\tan \α-\tan \β}$
None of these

Validate

Solution:

(2)

Let height of tower = BC = y metre
AB = height of flag-staff = h metre
∠BDC = α; ÐADC = β
Let, CD = x metre
In ΔBCD,

\tan \α= { {BC}}/{ {CD}}

⇒ \tan \α= {y}/{x}

⇒ x= {y}/{\tan \α}..... (i)

\ln \Δ A C D

\tan \β= {A C}/{C D}

⇒ \tan \β= {h+y}/{x}

⇒ x= {h+y}/{\tan \β}..... (ii)

∴{y}/{\tan \α}= {h+y}/{\tan \β}

⇒ y \tan \β=h \tan \α+y \tan \α

⇒ y \tan \β-y \tan \α=h \tan \α

⇒ y(\tan \β-\tan \α)=h \tan \α

⇒ y= {h \tan \α}/{\tan \β-\tan \α}

Go to Question:

Prev Question

Next Question