Question

Aruna is facing towards West, turning to her right
she walks 90 m, then turns right and goes another
35 m. Then turning to the right, goes 60 m and then
turning to her left and goes 25 m. How far and in
which direction is she now from her starting point?​

Answer 1

Answer:

North East

Explanation:

.^90cm Turn left>25cm Now she is in northeast

Answer 2

The distance from starting point is $30 \sqrt{5}$miter and direction is$tan^-^1 (\dfrac{1}{2})$.

Explanation:

• To  solve such type of problems, we draw the figure as shown (attached).

• Aruna is standing at the origin (O) and starts the journey.

• First, she is facing towards west and turns to her right. It means, now she is facing towards north. She walks 90 miter. So the length of OA = 90 miter.

• Then, turns right i.e. towards east. Now, she goes 35 miter i.e. OB = 35 miter
• After that, she turns towards right i.e. towards south and goes 60 miter. So, BC = 60 miter

• Then, turning her left i.e. east. She goes 25 miter i.e. CD = 25 miter

• We are asked the distance between O and D and angle $\theta$.

Form the right angle triangle $\Delta ODE$,

• OE = 35 + 25 = 60 miter

• DE = 90 - 60 = 30 miter

• $DE = \sqrt{60^2 + 30^2} = 30 \sqrt{5}$ miter

• $tan \theta = \dfrac{30}{60}$

         $\theta = tan^-^1 (\dfrac{1}{2})$

So, the distance from starting point is $30 \sqrt{5}$miter and direction is$tan^-^1 (\dfrac{1}{2})$.