Question

If one leg of a triangle is 500 meters and the other one is 600 meters. How long is the hypotenuse ?

Answer 1

Hint: We explain the Pythagoras’ theorem. We express it with respect to the sides of a right-angle triangle. We use the values of the arms of the right angle to find the value of the hypotenuse.

Complete step by step answer:
Pythagora's 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’. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle ${{90}^{\circ }}$.

Let us assume the sides or arms containing the right angle are of value a and b.They are also called the base and the height. If the hypotenuse be c, then we can say
${{c}^{2}}={{a}^{2}}+{{b}^{2}}$
We have been given that the length of the one leg of a triangle is 500 meters and the other one is 600 meters. They are the base and heights of the triangle. We put the values in the equation of ${{c}^{2}}={{a}^{2}}+{{b}^{2}}$ to get the value of $c$.So,

${{c}^{2}}={{500}^{2}}+{{600}^{2}}\\
\Rightarrow{{c}^{2}} =250000+360000\\
\Rightarrow{{c}^{2}} =610000$
Taking root square value, we get
$c=\sqrt{610000}\\
\Rightarrow c =100\sqrt{61}\\
\therefore c =781.02$.

Hence, the length of the hypotenuse is $781.02$ meters.

Note: This one-step formulation may be viewed as a generalization of Pythagoras's theorem to higher dimensions. However, this result is really just the repeated application of the original Pythagoras's theorem to a succession of right triangles in a sequence of orthogonal planes.