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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
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i have five question
HOW TO ADD MIXED FRACTION
1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al
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