SOLUTION: the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b.

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Question 340929: the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b.
Answer by nerdybill(7384) About Me  (Show Source):
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the hypotenuse of a right triangle is twice as long as the height. determine the height as a function of the base b.
.
Because it is a "right triangle" we can apply Pythagorean theorem:
Let h = height of triangle
then
2h = hypotenuse
.
+%282h%29%5E2+=+h%5E2+%2B+b%5E2+
+4h%5E2+=+h%5E2+%2B+b%5E2+
+3h%5E2+=+b%5E2+
+h%5E2+=+b%5E2%2F3+
+h+=+sqrt%28b%5E2%2F3%29+
+h+=+b%2Asqrt%281%2F3%29+
+h+=+b%2Asqrt%283%29%2F3+