Question

solving applications using the pythagorean theorem
susan wants to purchase a 44 inch tv. she is told that this measurement refers to the diagonal of the
tv. she also knows the length of the tv is 38.28 inches.
figure a is a diagram of the information susan knows.
figure a

susan wants to know if the tv will fit in her entertainment center, but first she needs to know the height
of the tv.
what is the height of the tv susan is thinking about purchasing ?
in
round your result to two decimal places as needed.
if the space in her entertainment center is 23.96 inches high and 45 inches long, will the tv fit in her
entertainment center?
question help: video written example message instructor

Explanation:

Step1: Recall Pythagorean Theorem

For right triangle: $a^2 + b^2 = c^2$, where $c$ is diagonal, $a$ is length, $b$ is height.

Step2: Rearrange for height

$b = \sqrt{c^2 - a^2}$

Step3: Substitute given values

$b = \sqrt{44^2 - 38.28^2}$

Step4: Calculate squares

$44^2 = 1936$, $38.28^2 = 1465.3584$

Step5: Compute difference and square root

$b = \sqrt{1936 - 1465.3584} = \sqrt{470.6416} \approx 21.69$

Step6: Compare TV size to space

TV height ≈21.69 in ≤23.96 in; TV length 38.28 in ≤45 in.

Answer:

1. The height of the TV is $\boldsymbol{21.69}$ inches.
2. Yes, the TV will fit in her entertainment center.