Answer:
Length of the side AC = [tex]3 \sqrt{3}[/tex] units
Step-by-step explanation:
The given triangle ABC is a right triangle.
Here, AB = 6 units ( hypotenuse)
CB = 3 units (base)
Now, as the triangle is a right triangle, so by
PYTHAGORAS THEOREM
In a right triangle,
[tex](Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}[/tex]
So, here in ΔABC: [tex](BC)^{2} + (AC)^{2} = (AB)^{2}[/tex]
or, [tex](3)^{2} + (AC)^{2} = (6)^{2}[/tex]
⇒[tex]AC = \sqrt{36 - 9} = \sqrt{27} = 3 \sqrt{3}[/tex]
or, the length of the side AC = [tex]3 \sqrt{3}[/tex] units
Answer:
[tex]\textbf{The length of $AC$ = \large{$3\sqrt{3}$}}[/tex]
Step-by-step explanation:
Use Pythagoras Theorem.
For any right-angled triangle, with sides, [tex]\textup{$a, b, c$ we have:\\}[/tex]
[tex][tex]\begin{centre}$ a^2 + b^2 = c^2 $ \\\end{centre}[/tex][/tex]
where, [tex]$a , b $[/tex] are the length of the sides and [tex]$c$[/tex] is the hypotenuse.
Here, [tex]$AB$[/tex] is the hypotenuse and [tex]$AC$[/tex] and [tex]$CB$[/tex] are its sides. Therefore from Pythagoras Theorem we have:
[tex]$6^2 = 3^2 + AC^2$\\$\implies 36 = 9 + AC^2 $\\$\implies AC^2 = 27$\\$\implies AC = \sqrt{27} = 3\sqrt{3} \hspace{25mm} \textup{(Eliminating -27 as distance cannot be negative)}[/tex]
So, we say the length of the other side [tex]$AC$[/tex] is [tex]$3\sqrt{3}$[/tex] units.
