1. The measure of a big-screen television is given by the length of a diagonal across the screen. A 60 -inch television has a width of 48 inches. Find the height of the screen.

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UpStudy AI · Accepted Answer

To find the height of the screen, we can use the Pythagorean theorem. The diagonal of the television, the width, and the height form a right triangle, where the diagonal is the hypotenuse.

Let:
- $$ d = 60 $$ inches (the diagonal)
- $$ w = 48 $$ inches (the width)
- $$ h $$ = height (unknown)

According to the Pythagorean theorem:

$$
d^2 = w^2 + h^2
$$

Substituting the known values:

$$
60^2 = 48^2 + h^2
$$

Calculating the squares:

$$
3600 = 2304 + h^2
$$

Now, subtract $$ 2304 $$ from both sides:

$$
3600 - 2304 = h^2
$$

$$
1296 = h^2
$$

Now, take the square root of both sides to find $$ h $$:

$$
h = \sqrt{1296}
$$

$$
h = 36 \text{ inches}
$$

Thus, the height of the screen is **36 inches**.
The height of the screen is 36 inches.

1. The measure of a big-screen television is given by the length of a diagonal across the screen. A 60 -inch television has a width of 48 inches. Find the height of the screen.

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