Suppose a spider was able to create one thread that would extend from the top-right back corner of its tank to the bottom-left front corner. Approximately how long would that thread need to be for the tank below? The path of the spider's thread is shown with a red dotted line. Round your answer to the nearest tenth of an inch. With numbers of 35in,16in and 12in. The diagonal of the bottom of the tank is how many inches? To the nearest tenth of an inch, the length of the spider's thread is how many inches?
To find the length of the spider's thread, we can use the Pythagorean theorem. Let's label the dimensions of the tank as follows:
- The length of the tank from the top-right back corner to the bottom-left front corner is 35 inches (let's call this dimension A).
- The width of the tank from the top-left back corner to the bottom-right front corner is 16 inches (let's call this dimension B).
- The height of the tank from the bottom-left back corner to the top-right front corner is 12 inches (let's call this dimension C).
We can see that the diagonal of the bottom of the tank forms the hypotenuse of a right triangle with dimensions A and B. Therefore, we can use the Pythagorean theorem to find the length of the diagonal:
Diagonal of the bottom = √(A^2 + B^2)
Diagonal of the bottom = √(35^2 + 16^2)
Diagonal of the bottom = √(1225 + 256)
Diagonal of the bottom = √1481
Diagonal of the bottom ≈ 38.5 inches (rounded to the nearest tenth)
Now, to find the length of the spider's thread, we need to consider the hypotenuse of a right triangle with dimensions A, B, and C. We can use the Pythagorean theorem again:
Length of the spider's thread = √(A^2 + B^2 + C^2)
Length of the spider's thread = √(35^2 + 16^2 + 12^2)
Length of the spider's thread = √(1225 + 256 + 144)
Length of the spider's thread = √(1625)
Length of the spider's thread ≈ 40.3 inches (rounded to the nearest tenth)
So, the diagonal of the bottom of the tank is approximately 38.5 inches and the length of the spider's thread is approximately 40.3 inches.