The length of two sides of a right triangle are 5in and 8 in. What is the difference between the two possible length of the third side of the triangle? Round your answer to the nearest tenth

Answer:Difference between the two possible lengths of the third side of the triangle=[tex]3.2[/tex] inchesStep-by-step explanation:Case 1: For [tex]\triangle ABC[/tex]Given:AB=5 in BC=8 in AC= unknownUsing 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] inchesCase 2: For [tex]\triangle ABC[/tex]Given:AC=8 in BC=5 in AB= unknownUsing 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] inchesDifference between the two possible lengths of the third side of the triangle= [tex]9.43-6.24 = 3.19\approx 3.2[/tex] inches