Chapter 12, Problem 27CR

To determine

Tocalculate:The distance woman is far away from starting point.

Answer to Problem 27CR

The woman is far away from starting point by100 m.

Explanation of Solution

Given information:

A woman walks 20 m west, 100 m south, another 8 m west, and then 4 m north.

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

Horizontal distance $=20+8=28$

Vertical distance $=100-4=96$

Her path forms a right triangle with legs 28 m and 96 m.

The hypotenuse (distance from starting point) can be calculated by applying Pythagoras Theorem.

In a right angle triangle,we get

  $\begin{array}{l}{\left(h\right)}^2={\left(28\right)}^2+{\left(96\right)}^2\\ h^2=784+9216\\ h^2=10000\\ h=\sqrt{10000}\\ h=100\end{array}$

The woman is far away from starting point by 100 m.