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प्रश्न
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
उत्तर
The distance d between two points (x1, y1) and (x2, y2) is given by the formula.
`d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`
The two given points are (asinα, −bcosα) and (−acos α, bsin α)
The distance between these two points is
`d = sqrt((a sin alpha + a cos alpha)^2 + (- b cos alpha - bsin alpha)^2)`
`= sqrt(a^2(sin alpha + cos alpha)^2 + b^2(-1)^2(cos alpha + sin alpha))`
`= sqrt(a^2(sin alpha + cos alpha)^2 + b^2(sin alpha + cos alpha))`
`= sqrt((a^2 + b^2)(sin alpha + cos alpha))`
`d = (sin alpha + cos alpha)sqrt(a^2 + b^2)`
Hence the distance is `(sin alpha + cos alpha)sqrt((a^2 + b^2))`
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
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- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
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