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Question
Find the angle subtended at the origin by the line segment whose end points are (0, 100) and (10, 0).
Solution
Let the given points be A(0,100), B(10,0) and the origin be denoted by o(0,0)
We know that
In a right angled triangle the angle oppposite the hypotenuse subtend an angle of 90°
Let us find distance AB, AO, BO
`AB = sqrt((10 - 0)^2 + (0 - 100)^2)`
`= sqrt(100 + 10000)`
`= sqrt(10100)` units
`AO = sqrt((0 - 0)^2 + (0 - 100)^2)`
= `sqrt(100)` untis
Her we can see that, `AO^2 + BO^2 = AB^2`
Therefore, ΔAOB is a right angled triangle with AB being the hypotenuse.
So the angle subtended at the origin by the giving line segment is 90°
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