Answer
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Hint: In this problem we have to use the Pythagorean Theorem to find the missing side of the right triangle with the given measures given c is the hypotenuse and we have a = 3, c = 4. We know that the Pythagoras Theorem is \[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\]. We can see that, we are already given the value for a and c, which we can substitute in the formula where the missing side is b, which we have to find.
Complete step-by-step answer:
We know that we have used the Pythagorean Theorem to find the missing side of the right triangle with the given measures given c is the hypotenuse and we have a = 3, c = 4.
We know that the Pythagoras Theorem is \[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\].
We can substitute the value a = 3, c = 4 in the above formula, we get
\[\Rightarrow {{3}^{2}}+{{b}^{2}}={{4}^{2}}\]
We can now simplify the above step, we get
\[\begin{align}
& \Rightarrow {{b}^{2}}=16-9 \\
& \Rightarrow {{b}^{2}}=7 \\
\end{align}\]
We can now take square root on both sides, we get
\[\Rightarrow b=\sqrt{7}\]
Therefore, the missing side of the given right triangle is \[\sqrt{7}\]units.
Note: Students should remember the Pythagoras theorem formula is \[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\]. Where the sum of squares of two sides is equal to the square of the hypotenuse. We should also see that the given triangle should be a right angle triangle, where Pythagoras theorem is only applied to right-angled triangles. We can also consider a as the perpendicular and find b as the base as it will lead to the same answer.
Complete step-by-step answer:
We know that we have used the Pythagorean Theorem to find the missing side of the right triangle with the given measures given c is the hypotenuse and we have a = 3, c = 4.
We know that the Pythagoras Theorem is \[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\].
We can substitute the value a = 3, c = 4 in the above formula, we get
\[\Rightarrow {{3}^{2}}+{{b}^{2}}={{4}^{2}}\]
We can now simplify the above step, we get
\[\begin{align}
& \Rightarrow {{b}^{2}}=16-9 \\
& \Rightarrow {{b}^{2}}=7 \\
\end{align}\]
We can now take square root on both sides, we get
\[\Rightarrow b=\sqrt{7}\]
Therefore, the missing side of the given right triangle is \[\sqrt{7}\]units.
Note: Students should remember the Pythagoras theorem formula is \[{{a}^{2}}+{{b}^{2}}={{c}^{2}}\]. Where the sum of squares of two sides is equal to the square of the hypotenuse. We should also see that the given triangle should be a right angle triangle, where Pythagoras theorem is only applied to right-angled triangles. We can also consider a as the perpendicular and find b as the base as it will lead to the same answer.