a ladder rest against a wall at an angle alpha to the horizontal its foot is pulled away from the wall through a distance A so that it slides a distance B down the wall making an angle beta with the horizontal.show that a/b=cos(alpha)-cos(beta)/sin(beta)-sin(alpha)

Asked by Muhammed Musthafa | 21st Feb, 2014, 09:46: PM

Expert Answer:

Consider the following figure,
 
 
 
begin mathsize 16px style Let space space XY equals WZ equals straight h space be space the space height space of space the space ladder.
Consider space the space triangle space OXY.
sinα equals OY over XY
sinα equals OY over straight h
OY equals hsinα
cosα equals OX over XY
cosα equals OX over straight h
OX equals hcosα
Consider comma space increment OWZ
sinβ equals OZ over WZ
sinβ equals OZ over straight h
OZ equals hsinβ
cosβ equals OW over WZ
cosβ equals OW over straight h
OW equals hcosβ
From space the space figure space it space is space clear space that
straight A equals OW minus OX
straight B equals OY minus OZ
straight A over straight B equals fraction numerator OW minus OX over denominator OY minus OZ end fraction
straight A over straight B equals fraction numerator cosβ minus cosα over denominator sinα minus sinβ end fraction
straight A over straight B equals fraction numerator cosα minus cosβ over denominator sinβ minus sinα end fraction end style

Answered by  | 28th Nov, 2017, 02:26: PM