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

Interpretations of derivatives, Interpretations of derivatives. Exampl...

Interpretations of derivatives. Example:   Find out the equation of the tangent line to                                       x 2 + y 2   =9 at the point (2, √5 ) .

Negative function , Negative function : Several functions are not positive...

Negative function : Several functions are not positive however.  Consider the case of f (x ) =x 2 - 4 on [0,2].  If we utilizes n = 8 and the midpoints for the rectangle height w

Young entrepreneur, As a creative and innovative entrepreneur, we are requi...

As a creative and innovative entrepreneur, we are required to invent or improvise a product or service that benefits the society and the economy, so what do you think is it?

Interval of convergence - sequences and series, Interval of Convergence ...

Interval of Convergence After that secondly, the interval of all x's, involving the endpoints if need be, for which the power series converges is termed as the interval of conv

Help, how do i know what operation to use in a fraction word problem

how do i know what operation to use in a fraction word problem

Solution set of equation, The complete set of all solutions is called as th...

The complete set of all solutions is called as the solution set for the equation or inequality.  There is also some formal notation for solution sets.  We have to still acknowledge

Marketing of herbal products , To help Himalya herbal launch a successful m...

To help Himalya herbal launch a successful marketing campaign in the UK

Find out primes of each denominator, Find out primes of each denominator: ...

Find out primes of each denominator: Add 1/15 and 7/10 Solution: Step 1:             Find out primes of each denominator. 15 = 5 x 3 10 = 5 x 2 Step 2:

Solving multi step equations, can you help me? cause im in 7th grade advanc...

can you help me? cause im in 7th grade advanced math and tomorrow I have a test tomorrow and I don''t get this

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