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

Linear programming , use the simplex method to solve the following lp probl...

use the simplex method to solve the following lp problem. max z = 107x1 + x2 + 2x3 subject to 14x1 + x2 - 6x3 + 3x4 = 7 16x1 + x2 - 6x3 3x1 - x2 - x3 x1,x2,x3,x4 > = 0

Radius of rhim, how long is the radius of car tyre?

how long is the radius of car tyre?

How did they go about "modernizing" the region, What were the two main poli...

What were the two main political parties that formed in the majority of the new nations of Latin America post independence? In what ways were they different? Which party ascended t

5th grader, my qustion is how do you muliply frations

my qustion is how do you muliply frations

Proof of the derivative of a constant, Proof of the Derivative of a Constan...

Proof of the Derivative of a Constant : d(c)/dx = 0 It is very easy to prove by using the definition of the derivative therefore define, f(x) = c and the utilize the definiti

Defining real numbers, The numbers used to measure quantities such as lengt...

The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers. Another definition of real numbers us

Properties of dot product - proof, Properties of Dot Product - proof P...

Properties of Dot Product - proof Proof of: If v → • v → = 0 then v → = 0 → This is a pretty simple proof.  Let us start with v → = (v1 , v2 ,.... , vn) a

Calculate area of a square, The area of a square is given by the formula wi...

The area of a square is given by the formula width time's height. But since the square has all the sides equal, the height is of the same measure as its width. Hence its formula 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