SOLUTION: given a right angled triangle, the hypotenuse is 70 and the sides have a ratio of 16 to 9, what are the lengths of the sides, please show the solution steps, so I can do the steps

Algebra ->  Triangles -> SOLUTION: given a right angled triangle, the hypotenuse is 70 and the sides have a ratio of 16 to 9, what are the lengths of the sides, please show the solution steps, so I can do the steps       Log On


   

Question 935304: given a right angled triangle, the hypotenuse is 70 and the sides have a ratio of 16 to 9, what are the lengths of the sides, please show the solution steps, so I can do the steps for other hypotenuse lengths. Thank you.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the sides +a+ and +b+, where
+a%2Fb+=+16%2F9+
------------------
By the pythagorean theorem:
+70%5E2+=+a%5E2+%2B+b%5E2+
+4900+=+a%5E2+%2B+b%5E2+
---------------------
+a%2Fb+=+16%2F9+
Multiply both sides by +9b+
+9a+=+16b+
+a+=+%28+16%2F9+%29%2Ab+
------------------
By substitution:
+4900+=+%28+16%5E2+%2F+9%5E2+%29%2Ab%5E2++%2B+b%5E2+
+4900+=+%28+256+%2F+81+%29%2Ab%5E2+%2B+%28+81%2F81+%29%2Ab%5E2+
+4900+=+%28+337%2F81+%29%2Ab%5E2+
+b%5E2+=+%28+81%2F337+%29%2A4900+
+b+=+%28+9%2A70+%29+%2F+sqrt%28337%29++
+b+=+630+%2F+18.358+
+b+=+34.32+
--------------
+a%2Fb+=+16%2F9+
+a+=+%28+16%2F9+%29%2Ab+
+b+=+%28+16%2F9+%29%2A34.32+
+b+=+61.01+
----------------
check answers:
+4900+=+a%5E2+%2B+b%5E2+
+4900+=+61.01%5E2+%2B+34.32%5E2+
+4900+=+3722.63+%2B+1177.86+
+4900+=+4900.49+
Error due to rounding off, I think