Answer:
[tex]c=\sqrt{13}[/tex]
Step-by-step explanation:
Given right triangle ABC.
Measure of leg BC = [tex]a=2[/tex]
Measure of leg AC = [tex]b=3[/tex]
To find the hypotenuse AB = [tex]c[/tex]
Solution:
Applying Pythagorean theorem.
[tex]Hypotenuse ^2= Leg1^2 + Leg 2^2[/tex]
For the given triangle :
[tex]AB^2=BC^2+AC^2[/tex]
[tex]c^2=a^2+b^2[/tex]
Plugging in the given values.
[tex]c^2=2^2+3^2[/tex]
[tex]c^2=4+9[/tex]
[tex]c^2=13[/tex]
Taking square root both sides.
[tex]\sqrt{c^2}=\sqrt{13}[/tex]
∴ [tex]c=\sqrt{13}[/tex] (Answer)
