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

6thgrade, do you have 3 digit and 4 digit number problem

do you have 3 digit and 4 digit number problem

How many days are there in a year, There are m months in a year, w weeks wi...

There are m months in a year, w weeks within a month and d days in a week. How many days are there in a year? In this problem, multiply d and w to obtain the total days in one

Angles, how to measure missing angle of an adjacent angle

how to measure missing angle of an adjacent angle

Mensuration, How do mensuration relate to the real life issues

How do mensuration relate to the real life issues

H, 6987+746-212*7665

6987+746-212*7665

H, 6987+746-212*7665

6987+746-212*7665

Quadric surfaces - three dimensional spaces, Quadric Surfaces Earlier w...

Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several

Find the derivatives, Find the derivatives of the following functions a)...

Find the derivatives of the following functions a)      y = 5x 4 +3x -1-x 3 b)      y = (x+1) -1/2 c)      y= e x2+1 d)     y= e 3x lnx e)     y =ln(x+1/x)y

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