Question

Meeru had lost her way home and was standing $25$meters away from her house in the southwest direction. She walks $20$meters north and reaches point A. How far and in which direction would she have to walk to reach her house?

Answer 1

Step 1: Draw a rough diagram as per the given information.

Here a right-angled triangle ABC is formed with hypotenuse AB of the length of $25$ meters and AC of the length of $20$meters

Thus she has to walk CB distance in the East direction to reach her house.

Step 2: Use the Pythagoras theorem to find the length of AB.

As Pythagoras' theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

$$\begin{gathered} C{B}^2+C{A}^2=A{B}^2 \\ \Rightarrow C{B}^2+{20}^2={25}^2 \\ \Rightarrow C{B}^2+400=625 \\ \Rightarrow C{B}^2=625-400 \\ \Rightarrow CB=\sqrt{225} \\ \Rightarrow CB=15\mathrm{meter} \end{gathered}$$

Hence she has to walk 15 meters in the East direction to reach her house.