A man walks 5m due north, then 5m due east. What is the distance from the starting point to the end point?

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to solve this problem:

The problem describes a right-angled triangle where:

The height of the pole is one leg, $a = 12$ m.
The length of the wire is the hypotenuse, $c = 15$ m.
The distance from the pole to the point where the wire is fixed to the ground is the other leg, $b = x$ .

Apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse ( $c$ ) is equal to the sum of the squares of the other two sides ( $a$ and $b$ ).
$a^2 + b^2 = c^2$
Substitute the given values:
$12^2 + x^2 = 15^2$
Calculate the squares of the known values.
$144 + x^2 = 225$
Isolate $x^2$ by subtracting 144 from both sides of the equation.
$x^2 = 225 - 144$ $x^2 = 81$
Take the square root of both sides to find the value of $x$ .
$x = \sqrt{81}$ $x = 9$
The distance from the pole to the point where the wire is fixed to the ground is $\boxed{\text{9 m}}$ .

Answer