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The altitude of a triangle is 4 meters. Express the base b as a function of the hypotenuse h and state the domain.
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Not enough info, or incorrect using the terms, or doesn't make sense.
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Your formulation is extremely bad.
1. If the triangle is right-angled, then the first phrase must be: "In an right-angled triangle, . . . "
2. If the triangle is right-angled, then its sides containing the right angle are called "legs".
In a right-angled triangle they never are called "base".
In an right-angled triangle they never are called "altitude".
In an right-angled triangle the "altitude" is the perpendicular from the vertex drawn to the hypotenuse.
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Probably, you are seeking for b = .
But with such formulation I can not be confident in anything.