To find the height of the TV when you know the width and the diagonal (which is the size of the TV), you can use the Pythagorean theorem. The relationship can be expressed as:
\[ d^2 = w^2 + h^2 \]
where:
- \( d \) is the diagonal (20 inches),
- \( w \) is the width (12 inches),
- \( h \) is the height.
Plugging in the values we know:
\[ 20^2 = 12^2 + h^2 \]
Calculating the squares:
\[ 400 = 144 + h^2 \]
Subtracting 144 from both sides gives:
\[ 400 - 144 = h^2 \]
\[ 256 = h^2 \]
Taking the square root of both sides:
\[ h = \sqrt{256} = 16 \]
So, the height of the 20-inch TV is 16 inches.
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