Prove that its inclination theta to the horizontal, Mathematics

Assignment Help:

Two stations due south of a tower, which leans towards north are at distances 'a' and 'b' from its foot. If α and β be the elevations of the top of the tower from the situation, Prove that its inclination 'θ' to the horizontal given by

cotΘ =  (bcot α - α cot β) / b-a

1099_horizontal.png

Ans:    Let AB be the leaning tower and C and D be the given stations. Draw BL ⊥ DA produced.

Then, ∠BAL = 0, ∠BCA = α, ∠BDC = a and DA = b.

Let AL = x and BL = h

In right ΔALB, we have :

AL/BL = Cot θ ⇒ x/h = Cot θ

⇒  x/h = Cot θ ⇒ x = h cot θ             .....(i)

In right ΔBCL, we have :

CL/BL = Cot α ⇒ a + x = h cot α

⇒ a = h (cot α - cot θ)

⇒ h =a / (cot α - cot θ)             ...(ii)

In right ΔBDL, we have :

DL/BL = cot β ⇒ DA + AL/BL = cot β

⇒ b + x/h = cot β ⇒ b + x = b cot β

⇒ b = h ((cot β - cot θ)           [using (i)]

⇒ h = b/(cot β - cotθ )       ...........(iii)

equating the value of h in (ii) and (iii), we get:

a/(cot α - cot θ )= b /(cot β - cotθ )

⇒ a cot β - a cot θ = b cot α - b cot θ

⇒ (b - a) cot θ = b cot α - a cotβ

⇒ cot θ = b cot α - a cot βθ/(b - a)


Related Discussions:- Prove that its inclination theta to the horizontal

Numerical analysis, just give me some tips to submit a good asignments

just give me some tips to submit a good asignments

Find out the probability, A speaks truth in 80% of the cases and B speaks t...

A speaks truth in 80% of the cases and B speaks truth in 60% of the cases.  Find out the probability of the cases of which they are possible to contradict each other in stating sim

Assumptions of interpolation and extrapolation, Assumptions The f...

Assumptions The figures known are assumed to be a normal series, that is a series without any violent, unexplained fluctuations in the values. The

Multiple, what number does not belong 43,47,53,59,65,67

what number does not belong 43,47,53,59,65,67

Initial value problems, Write a Matlab function MyIVP that solves an initia...

Write a Matlab function MyIVP that solves an initial-value problem (IVP) for a system of ordinary differential equations (ODEs) of the form x ?(t) = f (t, x(t)), where f : R × Rn ?

Think smarter, compare: 643,251; 633,512; and 633,893. the answer is 633,51...

compare: 643,251; 633,512; and 633,893. the answer is 633,512. what is the question?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd