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

Formula to computing how much lumber to buy, Audrey is creating a increased...

Audrey is creating a increased flowerbed which is 4.5 ft by 4.5 ft. She requires computing how much lumber to buy. If she requires knowing the distance around the flowerbed, which

Variation of parameters, In the previous section we looked at the method of...

In the previous section we looked at the method of undetermined coefficients for getting a particular solution to p (t) y′′ + q (t) y′ + r (t) y = g (t)    .....................

Find the sides of hypotenuse , The hypotenuse of a right triangle is 20m. ...

The hypotenuse of a right triangle is 20m. If the difference between the length of the other sides is 4m. Find the sides. Ans: APQ x 2 + y 2 = 202 x 2  + y 2 = 400

Simplex table, maximize Z=2x+5y+7z, subject to constraints : 3x+2y+4z =0

maximize Z=2x+5y+7z, subject to constraints : 3x+2y+4z =0

Polar coordinates - parametric equations & polar coordinates, Polar Coordin...

Polar Coordinates Till this point we've dealt completely with the Cartesian (or Rectangular, or x-y) coordinate system.  Though, as we will see, this is not all time the easie

Case study, considring the concept of product life cycle,where would you pu...

considring the concept of product life cycle,where would you put viedo games in thier life cycle?

Solve sin (a /7) =0 trig function, Solve sin (α /7) =0 . Solution B...

Solve sin (α /7) =0 . Solution By Using a unit circle it isn't too difficult to see that the solutions to this equation are, α /7 = 0 + 2 ? n     ⇒   α = 14 ? n

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

Project, elliptical path of celestial bodies

elliptical path of celestial bodies

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