Show that cos - cos /sin - sin = a/b, Mathematics

Assignment Help:

A ladder sets against a wall at an angle α to the horizontal.  If the foot is pulled away from the wall through a distance of 'a', so that is slides a distance 'b' down the wall making an angle β with the horizontal. Show that cosα - cos β/sin β - sin α = a/b

Ans:    Let CB = x m. Length of ladder remains same

Cos α = CB/CA     ∴ ED = AC  Let Ed be

Cos α = x/h       ∴ ED = AC = h

x = hcos α                .........(1)

cos β =DC + CB/ED

cos β = a + x/h

a + x = hcos β

x = hcos β - a              .........(2)

from (1) & (2)

hcos α = hcos β - a

hcos α - hcos β = - a

-a = h(cosα - cosβ)      .........(3)

Sin α = Sin α = AE + EB/AC

Sin α =b + EB/ h

hSin α - b = EB

EB = hSin α - b          .........(4)

Sin β = EB /DE

Sin β = EB/h

EB = hSin β             .........(5)

From (4) & (5)

hSin β = hSin α - b

b = hsin α - hSin β

-b = h(Sin β - Sin α)   .........(6)

Divide equation (3) with equation (6)

- a/-b = h(cosα - cos β )/ h(sin β - Sinα )

∴ a/b = Cosα - Cosβ/Sinβ - Sinα


Related Discussions:- Show that cos - cos /sin - sin = a/b

Index numbers, What are advantages and disadvantages of both Laspeyres and ...

What are advantages and disadvantages of both Laspeyres and Paasche?

Discontinuous integrand- integration techniques, Discontinuous Integrand- I...

Discontinuous Integrand- Integration Techniques Here now we need to look at the second type of improper integrals that we will be looking at in this section.  These are integr

Determines the angles of depression, A pilot is flying over a straight leng...

A pilot is flying over a straight length of road. He determines the angles of depression of two mileposts, 5 miles apart, to be 32° and 48°. a) Find the distance of the plane f

Bar charts, I''m supposed to be writing a critique for my maths project whe...

I''m supposed to be writing a critique for my maths project where i compare the prices for different holidays. i don''t know what to write for a critique though, any tips on what w

DIFFERENTIAL EQUATION, Find an integrating factor for the linear differenti...

Find an integrating factor for the linear differential equation and hence Önd its general solution: SOLVE T^ 2 DY DX+T2

Parallel lines, Parallel to the line specified by 10 y + 3x= -2 In this...

Parallel to the line specified by 10 y + 3x= -2 In this case the new line is to be parallel to the line given by 10 y ? 3x ? -2 and so it have to have the similar slope as this

Operation research, advantages of vogel''s approximation method over north ...

advantages of vogel''s approximation method over north west corner method

Shares and dividends, at what price 6.25% rs 100 share be quoted when the m...

at what price 6.25% rs 100 share be quoted when the money is worth 5%

Percents, If 2/3 of a number is 24 then 1/4 of a number is...

If 2/3 of a number is 24 then 1/4 of a number is...

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