Question

How do you find the missing side c given $ 3ft $ $ 4ft $ using the Pythagorean Theorem?

Answer 1

Hint: Here we use the Pythagoras theorem $ {c^2} = {a^2} + {b^2} $ to find the answer for this question. Here we are given with two sides ‘a’ and ‘b’ and to find the missing third side ‘c’ we use the Pythagoras theorem. The Pythagoras formula is given by $ {c^2} = {a^2} + {b^2} $ . Using this formula we substitute the values of ‘a’ and ‘b’ and we find the value of $ {c^2} $ and then find the square root of the $ {c^2} $ to finally yield the answer of the missing third side that we want.

Complete step by step solution:
The Pythagoras theorem states that
 $ {c^2} = {a^2} + {b^2} $
Substituting the values of ‘a’ and ‘b’ that is given in the problem
 $ {c^2} = {(3)^2} + {(4)^2} $
 $ {c^2} = 9 + 16 $
Now we add both the above values to get the resultant value
 $ {c^2} = 25 $
Now taking the square root of the value on both sides we get,
 $ \sqrt {{c^2}} = \sqrt {25} $
 $ c = 5 $

Hence, the value of the missing third side ‘c’ is given by $ c = 5 $

Note: We must know that the Pythagoras theorem is applicable only for right angle triangles and not for any other triangles. Here we must note that after getting the value of $ {c^2} $ it is important to take the square root to obtain the real value of the missing side. And also note that the side opposite to the right angle is the largest side of that particular triangle. So here in this case the angle opposite to the side ‘c’ is the right angle, since it is the largest side of the triangle.
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