SOLUTION: For the right triangle shown, the lengths of two sides are given. Find the third side. Leave your answer in simplified, radical form. b=9, c=16 a=

Algebra ->  Triangles -> SOLUTION: For the right triangle shown, the lengths of two sides are given. Find the third side. Leave your answer in simplified, radical form. b=9, c=16 a=      Log On


   

Question 378926: For the right triangle shown, the lengths of two sides are given. Find the third side. Leave your answer in simplified, radical form.
b=9, c=16
a=
Found 2 solutions by ewatrrr, Alan3354:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

right triangle, b=9, c=16 

APPLYING THE PYTHAGOREAN THEOREM TO SOLVE FOR a

a%5E2+%2B+b%5E2+=+c%5E2

a%5E2+%2B+9%5E2+=+16%5E2

a%5E2+=+16%5E2+-+9%5E2

a%5E2+=+256+-+81

a%5E2+=+175

a = ±sqrt%28175%29  Note: Negative solution cannot be used for length

a = sqrt%28175%29

a = sqrt%2825%2A7%29

a = 5%2Asqrt%287%29, in simplified, radical form

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If c is the longest side, the hypotenuse:
a+=+sqrt%2816%5E2+-+9%5E2%29
a+=+sqrt%28175%29+=+5sqrt%287%29