Question 1119395: Expresss the function as a formula:
the altitude of a right triangle as a function of the base if the hypotenuse is given
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the right triangle is composed of the altitude and the base and the hypotenuse.
the pythagorus formula states that the hypotenuse squared is equal to the altitude squared plus the base squared.
if you let h = the hypotenuse and b equal the base and a equal the altitude, then the formula becomes:
h^2 = a^2 + b^2
if you want to solve for the altitude, then do the following:
subtract b^2 from both sides of the equation to get:
h^2 - b^2 = a^2
solve for a^2 to get:
a^2 = h^2 - b^2
solve for a to get:
a = plus or minus sqrt(h^2 - b^2).
since a can't be negative, then the solution is:
a = sqrt(h^2 - b^2).
if the value of the hypotenuse is given, then let v = the value of the hypotenuse to get the formula to become:
a = sqrt(v^2 - b^2).
for example, if the hypotenuse is given as 5, then the formula for altitude becomes:
a = sqrt(5^2 - b^2).
since the hypotenuse is fixed at 5, then the value of the altitude is dependent on the value of the base.
for example:
if the value of the base is equal to 3, then the formula becomes:
a = sqrt(5^2 - 3^2) which becomes a = sqrt(25-9) which becomes a = sqrt(16) which becomes a = 4.
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