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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
product line of lg company
y=mx+c
a data set has a mean of 3, a median of 4, and a mode of 5.which number must be in the data set-3,4,5?
Before going further, let us repeat an aspect of learning which is useful to keep in mind while formulating teaching strategies. A child who can add or subtract in the context of s
methodology of OR
a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit
Find out primes of each denominator: Add 1/15 and 7/10 Solution: Step 1: Find out primes of each denominator. 15 = 5 x 3 10 = 5 x 2 Step 2:
conclusion for the shares nd dividends
what is 8x6 is
A recipe calls for 2 1/4 teaspoons of salt for every 1 1/8 teaspoons of black pepper used. How many teaspoons of salt are needed for each teaspoon of pepper used ?
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