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

Application of statistics-quality control, Quality Control Normally th...

Quality Control Normally there is a quality control departments in every industry which is charged along with the responsibility of ensuring about the products made do meet th

Formulas, how many formulas there for the (a-b)2

how many formulas there for the (a-b)2

Expected opportunity loss or eol method, Expected opportunity loss or EOL m...

Expected opportunity loss or EOL method EOL method is aimed at minimizing the expected opportunity loss or OEL. The decision maker chooses the strategy along with the minimum e

Using substitution solving polynomial equations, Using Substitution Solving...

Using Substitution Solving Polynomial Equations ? Solve : (x 3 + 4) 2 - 15 (x 3 + 4) + 36 = 0. You might be tempted to multiply everything out and factor. However, there

Find out the next number 320, Find out the next number in the subsequent pa...

Find out the next number in the subsequent pattern. 320, 160, 80, 40, . . . Each number is divided by 2 to find out the next number; 40 ÷ 2 = 20. Twenty is the next number.

Photogrammetry, basic linear algebra concepts and calculations in photogram...

basic linear algebra concepts and calculations in photogrammetry

Find out the variance and standard deviation, The probability of a rare dis...

The probability of a rare disease striking a described population is 0.003. A sample of 10000 was examined. Determine the expected no. suffering from the disease and thus find out

Show basic trigonometric functions, Q. Show basic Trigonometric Functions? ...

Q. Show basic Trigonometric Functions? Ans. There are six trigonometric functions and they can be defined using a right angle triangle. We first label each side according

Differentiate inverse tangent functions, Differentiate the following functi...

Differentiate the following functions. (a) f (t ) = 4 cos -1 (t ) -10 tan -1 (t ) (b)  y = √z sin -1 ( z ) Solution (a) Not much to carry out with this one other

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