Question

How do you solve the right triangle ABC given $a = 5$ and $b = 12$?

Answer 1

Hint:The given question requires to solve the right angled triangle given the length of two of its sides as $5cm$ and $12cm$. We have to find the length of the third side of the given right angled triangle. This can be done easily using the Pythagoras theorem. However, we first need to know the position of the right angle in the right angled triangle before applying the Pythagoras theorem.

Complete step by step solution:
Considering the given right angle is right angled at C, that is $\angle C = {90^\circ }$
Then side AC is named as ‘c’ and is the hypotenuse of the right angled triangle ABC given to us in the question.
Following the Pythagoras theorem, we have \[{\left( {Hypotenuse} \right)^2} = {\left( {Base} \right)^2} + {\left( {Altitude} \right)^2}\].
So, applying the Pythagoras theorem in the given triangle ABC, we get, ${c^2} = {a^2} + {b^2}$.
So, ${c^2} = {(5)^2} + {(12)^2}$
$ \Rightarrow {c^2} = 25 + 144$
$ \Rightarrow {c^2} = 169$
$ \Rightarrow c = \pm 13$
Since, c represents the length of a side and length of a side cannot be negative.
Hence, Third side of the triangle ABC $ = c = 13$

Note: For solving such type of question, where we need to find the third side of a triangle using the Pythagoras theorem, we need to know the position of right angle in the triangle beforehand since we need to know which of the three sides is the hypotenuse of the right angled triangle and then apply the Pythagoras theorem \[{\left( {Hypotenuse} \right)^2} = {\left( {Base} \right)^2} + {\left( {Altitude} \right)^2}\].