Question

pythagorean theorem at best buy
television fun facts:

• tvs come in a wide variety of sizes from 22 inches up to 80 inches+
• tvs are measured by their diagonal length
• the aspect ratio tells the ratio between the height and length (i.e. 16:9)

draw what you know:
draw a sketch of a 48 - inch plasma television with a height of 23.5 inches. label all the measurements (side lengths & angles) you know from the given information.
solve it:
with the given information, can you use the pythagorean theorem to find the length of the 48 - inch television? show your work below.

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). For a TV (a rectangle), the diagonal is the hypotenuse, and the height and length are the legs. Let the height \(a = 23.5\) inches, diagonal \(c=48\) inches, and length \(b\) (what we need to find).

Step2: Rearrange the formula to solve for \(b\)

We know \(a^{2}+b^{2}=c^{2}\), so we can rearrange it to \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute the values

Substitute \(a = 23.5\) and \(c = 48\) into the formula:
First, calculate \(c^{2}-a^{2}\):
\(c^{2}=48^{2}=2304\)
\(a^{2}=23.5^{2}=552.25\)
Then \(c^{2}-a^{2}=2304 - 552.25=1751.75\)

Step4: Take the square root

Now, find \(b=\sqrt{1751.75}\approx41.85\) (rounded to two decimal places)

Answer:

The length of the 48 - inch television is approximately \(\boldsymbol{41.85}\) inches.