Final answer:
To find the length of the television given its diagonal dimension of 49 inches and a height of 27 inches, we use the Pythagorean theorem. The length comes out to be approximately 40.9 inches when calculated using the formula derived from the theorem.
Step-by-step explanation:
The question asks us to find the length of a television screen given its diagonal measurement and height. The dimensions of a television screen can be treated as a right-angled triangle, where the diagonal represents the hypotenuse, the height is one of the legs, and the length that we need to find is the other leg. We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In mathematical terms, the theorem is written as c^2 = a^2 + b^2. So, to find the length (b) of the television, we rearrange the formula to b = √(c^2 - a^2). Here, c=49 inches is the diagonal, and a=27 inches is the height.
Plugging in the values and solving for b, we get b = √(49^2 - 27^2). That comes out to b = √(2401 - 729), which simplifies to b = √(1672). When you calculate that, you find that b is approximately 40.9 inches, which is the length of the television screen to the nearest tenth of an inch.