a clock hangs on the wall. the wall is 71 ft and 9 inches long and 10 ft and f inches high. the night watchman notices that the hands of the clock are pointing in opposite directions and are parallel to one of the diagonals of the wall. what was the exact time
10 ft and f inches high
f inches?
To find the exact time, we need to determine the diagonal of the wall and figure out which direction the hands of the clock are pointing.
Let's start by finding the length of the diagonal of the wall using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Given:
Length of the wall = 71 ft 9 inches = 71.75 ft
Height of the wall = 10 ft f inches = 10.f ft
We need to convert the height to feet. Since 1 foot is equal to 12 inches, we can write the height as:
Height of the wall = 10 ft f inches = 10 + (f/12) ft
Applying the Pythagorean theorem, we have:
Diagonal of the wall = √((Length of the wall)^2 + (Height of the wall)^2)
= √((71.75 ft)^2 + (10 + (f/12) ft)^2)
Now, let's consider the hands of the clock. There are two possibilities: the clock hands point towards the longer diagonal or the shorter diagonal.
If the clock hands point towards the longer diagonal, we can assume that one hand points towards the top-right and the other hand points towards the bottom-left corners of the wall.
If the clock hands point towards the shorter diagonal, we can assume that one hand points towards the top-left and the other hand points towards the bottom-right corners of the wall.
Now, let's analyze both possibilities:
1. If the clock hands point towards the longer diagonal:
In this case, the two hands divide the diagonal of the wall into three segments: one on the right, one on the left, and one along the diagonal.
2. If the clock hands point towards the shorter diagonal:
In this case, the two hands divide the diagonal of the wall into two segments, one along the diagonal and one perpendicular.
At this point, we need additional information to determine the exact time. Could you please provide any additional details or constraints?