Question

kailash faces towards north turning to his right he walks 23 metres then turns to his left and walks 30 metres next he moves 25 meters to his right he then turns to his right again and walks 55meters finally he turns to right and moves 40 meters in which direction is he now from his startig point?

Answer 1

Thus, the distance from initial position is 26.24 meter and direction is  $tan^-^1\dfrac{8}{25}$.

Step-by-step explanation:

• Kailash faces towards North and standing on origin 'O'. (refer the figure -1)

• Turning to his right and walks 23 meters (OA).

• Then, turns his left and walks 30 meters (AB).

• Next, he moves 25 meters to his right. (BC)

• After that, he turns right and walks 55 meters. (CD)

• Finally, he turns right and moves 40 meters. (DE)

From the figure, we are asked the length of OE and the angle $\theta$.

• From the figure, we make the right angle triangle $\Delta OEF$. (refer the figure -2)

Apply Pythagoras theorem, we get;

• $OE^2 = OF^2 + FE^2$

        OE = $\sqrt{25^2 + 8^2}$

        OE = $\pm26.24$ meter

Since, it is length. So, we take positive.

• OE = 26.24 meter

Now, $tan\theta = \dfrac{8}{25}$

         $\theta = tan^-^1\dfrac{8}{25}$

Thus, the distance from initial position is 26.24 meter and direction is  $tan^-^1\dfrac{8}{25}$.