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

Constructing a dfa/nfa or a regex), Let ∑ = (0, 1). Define the following la...

Let ∑ = (0, 1). Define the following language: L = {x | x contains an equal number of occurrences of 01 and 10} Either prove L is regular (by constructing a DFA/NFA or a rege

Mixing problems, In these problems we will begin with a substance which is ...

In these problems we will begin with a substance which is dissolved in a liquid. Liquid will be entering as well as leaving a holding tank. The liquid entering the tank may or may

Find the polynomial zeros , If two zeros of the polynomial f(x) = x 4 - 6x...

If two zeros of the polynomial f(x) = x 4 - 6x 3 - 26x 2 + 138x - 35 are 2 ± √3.Find the other zeros.     (Ans:7, -5) Ans : Let the two zeros are 2 +√3 and 2 - √3 Sum of

Show frequency tables, Q. Show Frequency Tables? Ans. A frequency ...

Q. Show Frequency Tables? Ans. A frequency table is used to show how often a piece of data occurs. Example: Michelle decides to keep track of the number of phone call

Plane and solid mensuration, the area of a triangle is 20 and its base is 1...

the area of a triangle is 20 and its base is 16. Find the base of a similar triangle whose area is 45. Given is a regular pentagon. Find the measure of angle LHIK.

Fraction, sarah has 12 gel pen. she gave 3/4. how many she have

sarah has 12 gel pen. she gave 3/4. how many she have

Muptipucation, if 2+2=4 what does two times two epual?

if 2+2=4 what does two times two epual?

Find the straight distance between a and b, There is a staircase as shown i...

There is a staircase as shown in figure connecting points A and B. Measurements of steps are marked in the figure. Find the straight distance between A and B. (Ans:10) A ns

What is a scatter diagram, What is a scatter diagram? A scatter diagram...

What is a scatter diagram? A scatter diagram is a graphical representation of data points for a particular sample. Choosing a dissimilar sample or enlarging the original one ca

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