To find the length of the spider's thread, we need to find the length of the diagonal of the bottom of the tank.
Using the Pythagorean theorem, we can find the length of the diagonal:
a^2 + b^2 = c^2
In this case, a and b represent the sides of the bottom of the tank, and c represents the length of the diagonal.
The sides of the bottom of the tank are 24 inches and 18 inches.
So, plugging these values into the Pythagorean theorem:
24^2 + 18^2 = c^2
576 + 324 = c^2
900 = c^2
Taking the square root of both sides to solve for c:
c = √900
c = 30 inches
Therefore, the diagonal of the bottom of the tank is 30 inches.
To find the length of the spider's thread, we can imagine that the thread forms a right triangle with the diagonal of the tank and the dotted line represents the hypotenuse of that triangle.
Using the Pythagorean theorem again, we can calculate the length of the spider's thread:
a^2 + b^2 = c^2
In this case, a and b represent the sides of the right triangle formed by the spider's thread, and c represents the length of the spider's thread.
One of the sides of the right triangle formed by the spider's thread is the diagonal of the tank, which we just calculated to be 30 inches.
The other side of the right triangle formed by the spider's thread is the distance from the top-right back corner of the tank to the bottom-left front corner.
By visual inspection, we can see that this distance is the same as the length of one side of the tank, which is 24 inches.
So, plugging these values into the Pythagorean theorem:
24^2 + b^2 = 30^2
576 + b^2 = 900
b^2 = 900 - 576
b^2 = 324
Taking the square root of both sides to solve for b:
b = √324
b = 18 inches
Therefore, the length of the spider's thread is 18 inches.
Rounded to the nearest tenth of an inch, the length of the spider's thread is 18.0 inches.
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.
(2 points)
The diagonal of the bottom of the tank is
inches. To the nearest tenth of an inch, the length of the spider's thread is
inches.
1 answer
1 answer