1800-150-456-789
FlagBACK
Flag Algebra> A vertical tower PQ stands at a point P. ...
question mark

A vertical tower PQ stands at a point P. Points A and B are located to the South and East of P respectively. M is the mid point ofAB PAM is an equilateral triangle; and N is the foot of the perpendicular from P on AB. Let AN = 20 meters and the angle of elevation of the top of the tower at N is tan-1 (2). Determine the height of the tower and the angles of elevation of the top of the tower at A and B.

Hrishant Goswami , 10 Years ago
Grade 10
anser 1 Answers
Jitender Pal

Last Activity: 10 Years ago

Hello Student,
Please find the answer to your question
Let PQ = h
As A and B are located to the south and east of P respectively,
∴ ∠APB = 90°. M is mid pt of AB. PAM is an equilateral ∆
235-874_12345.png
∴ ∠ APM = 60° :
Also PN ⊥ AB, therefore AN = NM = 20 m
⇒ AP = 40 m
Let angles of elevation of top of the tower from A, N and B be α, θ and β respectively. ATQ, tan θ = 2
In ∆ PQN tan θ = PQ/PN
⇒ 2 = h/PN ⇒ PN = h/2 . . . . . . . . . . . . . . . . . . . (1)
Also in ∆APM, ∠APM = 60° (being equilateral ∆) and PN is altitude ∴ ∠APN = 30°(as in equilateral ∆ altitude bisects the vertical angle.
∴ In ∆APN tan ∠ APN = AN/PN
⇒ tan 30°= 20 / h/2 [Using eq. (1)]
⇒ h/2√3 = 20 ⇒ h = 40√3m.
In ∆APQ tan α = h/AP ⇒ tan α = 40√3/40 = √3
⇒ α = 60° Also in ∆ABQ tan β = h/PB but in rt ∆PNB
PB = \sqrt{PN^2+NB^2} = \sqrt{(20\sqrt{3})^2+(60)^2}
∴ PB = √1200 + 3600 = √4800 = 40 √3
∴ tan β = 40 √3/40 √3 ⇒ tan β = 1 ⇒ β = 45°
Thus h = 40 √3m ; ∠’s of elevation are 60°, 45°

Thanks
Jitender Pal
askIITians Faculty

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 1 Year ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
0 Answer Available

Last Activity: 2 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 2 Years ago