The diagram for the given problem is shown below (making origin as initial position of the robot):
Now let's tilt the diagram by 11.299880 in clockwise direction. We will get this new diagram :
We have to calculate the value of OB . Here, OA = 10 m.
First we will derive equation of the line AB :
The coordinate of point A is (0 , 10).
The slope of the line AB can be calculated as
So, the equation of line AB can be written as
or, . ....................................(1)
Similarly, we can write equation of line OB.
The slope of OB will be
As the line OB passes through the origin (0 , 0), we can write the equation of the line OB as
or, ........................................(2)
Now, by solving equation (1) and (2), we can calculate the point of intersection of the line OB and AB or the coordinate of point B .
Putting the value of y from equation (2) in equation (1), wee get
or,
or,
Putting the value of x in equation (2), we get
So, the coordinate of point B is (12.020767 , 6.571999) .
Now, we can calculate the length of the line OB as
Hence, the robot is 13.70 m far away from its original position.
For any doubt please comment and please give an up vote. Thank you .
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