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 number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

Regression, regression line drawn as Y=C+1075x, when x was 2, and y was 239...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Which number falls among 5.56 and 5.81, Which number falls among 5.56 and 5...

Which number falls among 5.56 and 5.81? If you add a zero to the end of 5.6 to get 5.60, it is simpler to see that 5.56

find an explicit formula, (a) The generating function G(z) for a sequence ...

(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co

Hello, dans chaque cas recris l expression sous la forme d un rappot reduit...

dans chaque cas recris l expression sous la forme d un rappot reduit 5kg/600g

what is probability that point will be chosen from triagle, In the adjoini...

In the adjoining figure ABCD is a square with sides of length 6 units points P & Q are the mid points of the sides BC & CD respectively. If a point is selected at random from the i

Michael has 16 cds how many cds does kathleen have, Michael has 16 CDs. Th...

Michael has 16 CDs. This is four more than twice the amount that Kathleen has. How many CDs does Kathleen have? Let x = the number of CDs Kathleen has. Four more than twice th

The mean value theorem for integrals, The Mean Value Theorem for Integrals ...

The Mean Value Theorem for Integrals If f(x) is a continuous function on [a,b] then here is a number c in [a,b] thus, a ∫ b f(x) dx = f(c)(b -a) Proof Let's begin

Basic mathematics, I need help with my homework, I am to the edge right now...

I need help with my homework, I am to the edge right now with this w=5pq/2

Wholenumberriddles, I am less than 100 the sum of my digits is 4 half of me...

I am less than 100 the sum of my digits is 4 half of me is an odd 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