Question

the listed size of tv screens and monitors is the diagonal of the screen. a 10 - in tv set also has a width of 8 inches. what is its height? select the correct choice and fill in the answer box(es) to complete your choice. \\(\bigcirc\\) a. using radicals, b is exactly \\(\square\\). the b, up to three decimal places, is approximately \\(\square\\) \\(\bigcirc\\) b. the b is exactly \\(\square\\). no approximation is necessary.

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the diagonal of the right - triangle (in this case, the diagonal of the TV screen, \(c = 10\) inches) and \(a\) is the width (\(a=8\) inches), and \(b\) is the height.
Substitute the values into the formula: \(8^{2}+b^{2}=10^{2}\).

Step2: Solve for \(b^{2}\)

First, calculate \(8^{2}=64\) and \(10^{2} = 100\).
The equation becomes \(64 + b^{2}=100\).
Subtract 64 from both sides: \(b^{2}=100 - 64\).
So, \(b^{2}=36\).

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{36}\).
Since \(b>0\) (height cannot be negative), \(b = 6\) inches.

Answer:

B. The \(b\) is exactly \(6\). No approximation is necessary.