Pythagorean Theorem Word Problems
A certain television is advertised as a 36-inch TV (the diagonal length). If the width of the TV is 26 inches, how tall is the TV? Round to the nearest tenth of an inch.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the TV screen forms a right triangle, where the width of the TV is one side, the height of the TV is the other side, and the diagonal length is the hypotenuse. Let's call the height of the TV "h".
We can set up the equation using the Pythagorean theorem:
(26)^2 + h^2 = (36)^2
Simplifying, we get:
676 + h^2 = 1296
To isolate h^2 on one side of the equation, we subtract 676 from both sides:
h^2 = 620
Taking the square root of both sides, we find:
h ≈ 24.9
Therefore, the height of the TV is approximately 24.9 inches.