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

Explain what is symmetry in maths, Symmetry Definition : A line of sy...

Symmetry Definition : A line of symmetry divides a set of points into two halves, each being a reflection of the other. Each image point is also a point of the set. Defin

How to left shifts and right shifts a graph, Q. How to Left shifts and righ...

Q. How to Left shifts and right shifts a graph? Ans. When you're translating (shifting) a graph, it's easy to get subtracting and adding mixed up. It seems counter-intuiti

The number of filtering steps, The amount of particulate matter left in sol...

The amount of particulate matter left in solution during a filtering process is given by the equation p(n) = 500(2) -0.8n , where n is the number of filtering steps. Find the amoun

Solve following 4e1+3 x - 9e5-2 x = 0 logarithms, Solve following 4e 1+3 x...

Solve following 4e 1+3 x - 9e 5-2 x  = 0 . Solution Here the first step is to get one exponential on every side & then we'll divide both sides by one of them (that doesn'

Compound interest, some experts estimate that the cost of education in the ...

some experts estimate that the cost of education in the US increases by 6% p.a. An Ivy League college currently costs $24,502 for one year''s study today. Using compound interest r

Calculate what number of workers should be hired, You are given the followi...

You are given the following information about the amount your company can produce per day given the number of workers it hires. Numbers of Workers Quanti

How mathematical ideas grow, HOW MATHEMATICAL IDEAS GROW :  In this sectio...

HOW MATHEMATICAL IDEAS GROW :  In this section we shall consider three aspects of the nature of mathematical ideas, namely, that they progress from concrete to abstract, from part

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