Question

Find the angle subtended at the origin by the line segment whose end points are (0, 100) and (10, 0).

Answer 1

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(0 + 10000)`

= `sqrt(10000)` untis

Here 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 given line segment is 90°.