Final answer:
The maximum diagonal length of the TV Jake can fit in his cabinet is approximately 73 inches, calculated using the Pythagorean theorem with the cabinet width of 48 inches and height of 55 inches.
Step-by-step explanation:
To determine the maximum diagonal length of a TV that Jake can purchase to fit into his cabinet, we need to use the Pythagorean theorem. Since the TV has to fit within the dimensions of the cabinet, we are essentially looking for the hypotenuse of a right-angled triangle where the other two sides are the width and the height of the cabinet space available.
Steps to calculate the maximum diagonal length:
- First, consider the width and height as the legs of a right-angled triangle.
- The width of the cabinet is 48 inches and the height is 55 inches.
- According to the Pythagorean theorem: (Diagonal)^2 = (Width)^2 + (Height)^2
- Plug in the values: (Diagonal)^2 = (48)^2 + (55)^2
- Calculate the squares: (Diagonal)^2 = 2304 + 3025
- Sum the squares: (Diagonal)^2 = 5329
- Finally, take the square root to find the diagonal: Diagonal = √5329
- Diagonal = 73 inches (approximately).
The maximum diagonal length of the TV that Jake can purchase is approximately 73 inches.