wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

From a window (h metres high above the ground) of a house in a street, the angle if elevation and depression of the top and the foot of another house on the opposite side of the street are θ and ϕ respectively.
Find the height of opposite house if θ=60o,ϕ=45o,h=120metres.

A
317.84m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
366.97m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
301.44m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D None of these
Let L be the window of a house LM. Let PQ be the height of the opposite house such that, PQ= height of the opposite house =H metres. Then LM=hmetres. Through L draw LNPQ, meeting PQ at N. As per condition of the problem, PLN=θ,NLQ=ϕ, Let PQ=H metres then PN=(Hh)metres. Let LN=MQ=xmetres
(NQ=LM=hmetres)
From the right LNP,
PNLN=tanθ
Hhx=tanθ
x=Hhtanθ.......(1)
From the right LNQ
NQLN=tanϕ
hx=tanϕ
htanϕ=x.........(2)
From (1) and (2), we get:
Hhtanθ=htanϕ
Htanϕhtanϕ=htanθ
Htanϕ=h(tanϕ+tanθ)
Required height of opposite house.
=H=h(1+tanθcotϕ)
For θ=60o,ϕ=45o,h=120m,
The height of the opposite house
H=120(1+tan60ocot45o=120(1+3×1)
H=120(1+1.732)=120×2.732=327.84m
222837_239109_ans_bebfa4b937f4441db2e39dc5151b82c6.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Trigonometric Ratios
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon