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

Student, Patio measures 24 meters square. Patio stone are 30 cm each side. ...

Patio measures 24 meters square. Patio stone are 30 cm each side. How many stones are required to cover the patio?

Theory of equations, If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(...

If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(r+2)=

Simple equations, three times the first of the three consecutive odd intege...

three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.

Introduction To Numerical Methods & Matlab, Can you help me with the course...

Can you help me with the coursework i have in Matlab?

Nun, how do you identify area ??

how do you identify area ??

Determine the other two sides of the triangle, The radius of the in circle ...

The radius of the in circle of a triangle is 4cm and the segments into which one side is divided by the point of contact are 6cm and 8cm.  Determine the other two sides of the tria

Homogeneous differential equation, Assume that Y 1 (t) and Y 2 (t) are two ...

Assume that Y 1 (t) and Y 2 (t) are two solutions to (1) and y 1 (t) and y 2 (t) are a fundamental set of solutions to the associated homogeneous differential equation (2) so, Y

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