Flag Algebra> (i) PQ is a vertical tower. P is the foot...
question mark

(i) PQ is a vertical tower. P is the foot and Q is the top of the tower. A, B, C are three points in the horizontal plane through P. The angles of elevation of Q from A, B, C are equal, and each is equal to θ. The sides of the triangle ABC are a, b, cand the area of the triangle ABC is ∆. Show that the height of the tower isabc tan θ/A∆(ii) AB is a vertical pole. The end A is on the level ground. C is the middle point of AB. P is a point on the level ground. The portion CB subtends an angle β at P. If AP = n AB, then show that tan β = n/2n2 + 1

Simran Bhatia , 10 Years ago
Grade 11
anser 1 Answers
Aditi Chauhan

Last Activity: 10 Years ago

Hello Student,
Please find the answer to your question
(i) Let h be the height of tower PQ.
In ∆ APQ tan θ = h/AP ⇒ AP = h/tan θ
236-322_12345.png
Similarly in ∆’s BPQ and CPQ we obtain
BP = h/tan θ = CP
∴ AP = BP = CP
⇒ P is the circum centre of ∆ ABC with circum radius R = AP = abc/4∆
∴ h = AP tan θ = abc tan θ/4 ∆
(ii) Given AP = AB x n
⇒ AB/AP = 1/n = tan θ
∴ tan θ = 1/n
236-779_12345.png
Also tan (θ – β) = AC/AP = 1/2 AB/AP = 1/2n
⇒ tan θ – tan β/ 1+ tan θ tan β = 1/2n ⇒ \frac{\frac{1}{n}-tan\beta }{1+\frac{1}{n}tan \beta}= 1/2n
⇒ 2n – 2n2 tan β = n + tan β
⇒ (2n2 + 1) tan β = n ⇒ tan β = n/2n2 + 1

Thanks
Aditi Chauhan
askIITians Faculty

Provide a better Answer & Earn Cool Goodies

Enter text here...
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

Enter text here...