Question

How do you find b in the Pythagorean theorem given $a = 3$, $c = 4$ ?

Answer 1

Hint: Pythagorean or Pythagoras theorem states that “ In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the square of other two sides“.
Pythagoras theorem formula is \[\;hypotenus{e^2} = perpendicula{r^2} + bas{e^2}\]
In a right-angled triangle, if “ a ” denoted perpendicular, “ c “ denotes base and “ b “ denotes hypotenuse then the formula accordingly will be
${b^2} = {a^2} + {c^2}$
The side opposite to ${90^ \circ }$ is called the hypotenuse. It is also the longest side in comparison to the other two sides.

Complete step by step answer:
Here $a = 3$ and $c = 4$ is given .
Considering “ a ”, “ b “ and “ c” as sides of a right-angled triangle.
Applying the values of “ a “ and “ c “ in Pythagoras theorem
${b^2} = {a^2} + {c^2}$
$ \Rightarrow {b^2} = {(4)^2} + {(3)^2}$
Solving the above , squaring the numbers 4 and 3 . Square of 3 is 9 , square of 4 is 16
$ \Rightarrow {b^2} = 16 + 9$
Combine the terms
$ \Rightarrow {b^2} = 25$
Taking square root both sides
$ \Rightarrow b = \sqrt {25} $
We know square root of 25 is 5
$ \Rightarrow b = 5$

Thus , b = 5 units.

Additional information:
The answers can come different when “ a, b, c “ are denoted differently.
The hypotenuse formula is simply taking the Pythagorean or Pythagoras theorem and solving for hypotenuse The answers can come different when “ a, b, c “ are denoted differently.

Note:
Memorize the Pythagoras theorem formula.
Rearrange the equation to get the desirable variable before combining like terms and taking a square root. Check the formula then put the values given in question accordingly.
Try to write the values in brackets to make it easier to solve and be careful of positive and negative signs.