Answer:
Difference between the two possible lengths of the third side of the triangle=[tex]3.2[/tex] inches
Step-by-step explanation:
Case 1: For [tex]\triangle ABC[/tex]
Given:
AB=5 in BC=8 in AC= unknown
Using Pythagorean theorem:
[tex]AC^2=AB^2+BC^2[/tex]
[tex]AC^2=5^2+8^2[/tex] [Plugging in values of [tex]AB \ and\ BC[/tex]
[tex]AC^2=25+64\\AC^2=89[/tex]
Taking square root both sides.
[tex]\sqrt AC^2=\sqrt89\\AC=9.43[/tex] inches
Case 2: For [tex]\triangle ABC[/tex]
Given:
AC=8 in BC=5 in AB= unknown
Using Pythagorean theorem:
[tex]AB^2=AC^2-BC^2[/tex]
[tex]AB^2=8^2-5^2[/tex] [Plugging in values of [tex]AC \ and\ BC[/tex]
[tex]AB^2=64-25\\AB^2=39[/tex]
Taking square root both sides.
[tex]\sqrt AB^2=\sqrtB9\\AB=6.24[/tex] inches
Difference between the two possible lengths of the third side of the triangle= [tex]9.43-6.24 = 3.19\approx 3.2[/tex] inches
