My teacher challenged us to get the sides of right angled triangle with one side.
ABC is a right-angled triangle at B. AB is 6 cm long. Find AC and BC.
[Math] Solving right-angled triangle with one side
pythagorean triplestrigonometry
pythagorean triplestrigonometry
My teacher challenged us to get the sides of right angled triangle with one side.
ABC is a right-angled triangle at B. AB is 6 cm long. Find AC and BC.
Best Answer
I assume your teacher meant integer sides (otherwise it has an infinite solutions!!).
So,we can see that one side is $6$ units.
We know,$AB^2+BC^2=AC^2$.So,the three are Pythagorean triples.
We can generate Pythagorean triples in the following way.
$(m^2-n^2),2mn,(m^2+n^2)$ are three numbers which are Pythagorean triples for any integers $m,n$.
So,here we let,$2mn=6\implies mn=3$ Now,as $3$ is a prime it can be factorized only as $3\times1$.So,$m=3,n=1$.
Substituting these values into $(m^2-n^2)$ and $(m^2+n^2)$ we get $8,10$ respectively.So,the sides are $8,6,10$.
Hope this helps!!