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

Write down two more reasons why division is difficult, Write down two more ...

Write down two more reasons why children consider 'division' difficult. Regarding the first reason given above, one of fie few division related experiences that the child perhaps d

Cooking measurement question, Ask question what is half of 1 1/3 liquid mea...

Ask question what is half of 1 1/3 liquid measurements?

Fractions, A recipe calls for 2 1/4 teaspoons of salt for every 1 1/8 teasp...

A recipe calls for 2 1/4 teaspoons of salt for every 1 1/8 teaspoons of black pepper used. How many teaspoons of salt are needed for each teaspoon of pepper used ?

Example of imaginary numbers, Example of Imaginary Numbers: Example 1...

Example of Imaginary Numbers: Example 1: Multiply √-2  and √-32 Solution: (√-2)( √-32) = (√2i)( √32i) =√64 (-1) =8 (-1) =-8 Example 2: Divid

Understanding Logistics, How can i get a better understanding of logistics ...

How can i get a better understanding of logistics without having a degree on logistics and knowledge of it? Simply, in a very basic form..

Cylindrical coordinate system, how to describe the locus of the equation x^...

how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?

Area of polygons, ho we can find the area of diffrent types of polygon

ho we can find the area of diffrent types of polygon

Radicals, We'll include this section with the definition of the radical.  I...

We'll include this section with the definition of the radical.  If n is a +ve integer that is greater than one and a is a real number then, Where n is termed as the index,

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