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Find the Angle Subtended at the Origin by the Line Segment Whose End Points Are (0, 100) and (10, 0) - CBSE Class 10 - Mathematics

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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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Solution Find the Angle Subtended at the Origin by the Line Segment Whose End Points Are (0, 100) and (10, 0) Concept: Area of a Triangle.
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