Question: Theo has a rectangular space on his wall where he would like to put a small TV. He finds the perfect TV that measures $28.5$ inches wide and $16$ inches tall. His friend wants to know the diagonal size of his new TV. Using the Pythagorean Theorem, what is the length of the diagonal of the television, rounded to the nearest inch?
1. **State the problem:** We need to find the diagonal length of a TV that is $28.5$ inches wide and $16$ inches tall.
2. **Formula:** The Pythagorean Theorem states that for a right triangle with legs $a$ and $b$ and hypotenuse $c$, $$c = \sqrt{a^2 + b^2}$$
3. **Apply the formula:** Here, $a = 28.5$ and $b = 16$. So,
$$c = \sqrt{(28.5)^2 + (16)^2}$$
4. **Calculate squares:**
$$(28.5)^2 = 812.25$$
$$(16)^2 = 256$$
5. **Sum the squares:**
$$812.25 + 256 = 1068.25$$
6. **Find the square root:**
$$c = \sqrt{1068.25}$$
7. **Calculate the square root:**
$$c \approx 32.69$$
8. **Round to the nearest inch:**
$$c \approx 33$$
**Final answer:** The diagonal length of the TV is approximately $33$ inches.