Latest CAT Aptitude Question SOLUTION: A pole seen from a certain distance at an angle of 15 degrees and 100 meters ahead by 30 degrees. What is the height of pole ?

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A pole seen from a certain distance at an angle of 15 degrees and 100 meters ahead by 30 degrees. What is the height of pole ?

Asked In CAT kavita pandya (12 years ago)

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parvez akhtar  (12 years ago)

Solution:
Sol :Here distance by which 30 degree angle is made to look at the pole = X
Here distance by which 15 degree angle is made to look at the pole = 100+X
here, Tan 30= H/X ---------(1) //(where H is the height of pole)
Tan 15= H/(100+X)----------(2)
Solve for X : (H/Tan 30)=(H/Tan 15)-100 (Tan 30= 0.577, Tan 15= 0.26)
Answer : 33.33 app.

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amanpreet singh chawla  (8 years ago)

ans : h=50m

let height be h
let dis from 100m to base of pole be x

then,
tan 15` = h/(100+x) ------ (1)
tan 30` = h/x ------- (2)

from (2)
x=h/ tan(30`)
x= root(3)*h ---- (3)

also,
tan 15` = sin 30`/ (1+cos 30`)
tan 15` = 1/(2+root(3))

putting value of tan 15` and (3) in (1)

1/(2+root(3)) = h/(100+root(3)*h)
1/(2+root(3)) = 1/((100/h)+root(3))
(100/h)+root(3) = 2+root(3)
100/h = 2
h=50m

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jay baria  (12 years ago)

height of pole is say H
tan 15=H/x
tan 30=H/(x-100)
so .577=H/((H/.267)-100)

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