Prove that its inclination is given by cot = b cot - a, Mathematics

Assignment Help:

Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot.  If α ,  β be the elevations of the top of the tower from these stations, prove that its inclination ? is given by cot ? = b cot α - a cot β/b-a .

1751_Untitled1.png

Ans: Let AE = x, BE = h

Tan φ   =BE/AE =h/x

x= h x (1/tan φ)

x = h cot φ  ---------------1

tan α =BE/CE  = h /a + x

a + x = h cot α

x= h cot α - a --------------2

tan β = BE/DE = h/b + x

b+x = h cot β

x = h cot β - b ---------------3

from 1 and 2

h cot φ = h cot α - a

h ( cot φ  + cot α ) = a

h =  a /- cot φ + cot α -------------4

from 1 and 3

h cot φ = h cot β - b

h ( cot φ  - cot β) = b

h= b/- cot φ + cot β

from 4 and 5

a/- cot φ + cot α  = b/- cot φ + cot β

a (cot β - cot φ  ) = b ( cot α - cot φ )

-     a cot φ  + b cot φ  = b cot α - a cot β

(b - a) cot φ  = b cot α - a cot β

cot φ  = b cot α - a cot β/b - a


Related Discussions:- Prove that its inclination is given by cot = b cot - a

Complex Numbers, How do you compute the phase/angle of a complex number? i....

How do you compute the phase/angle of a complex number? i.e 1+2i

Minimizing the sum of two distances, The value of y that minimizes the sum ...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

Word problem, On a canoe trip. a person paddled upstream against the curren...

On a canoe trip. a person paddled upstream against the current ata an average of 2mi/h. the return trip with the current at 3mi/h. Need to find the paddling spped in still water an

How to subtract fractions with different denominators, Q. How to Subtract f...

Q. How to Subtract fractions with different denominators? Ans. As with adding fractions, you can't subtract unless the denominators are the same. Here is an example: 9/

What are the average total repair costs per month, An automobile manufactur...

An automobile manufacturer needs to build a data warehouse to store and analyze data about repairs of vehicles. Among other information, the date of repair, properties of the vehic

Describe square roots, Describe Square Roots? When a number is written ...

Describe Square Roots? When a number is written inside a radical sign (√), the number is called the radicand, and we say that you are "taking the square root of" that number.

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