Answer: 34.43 feet
Step-by-step explanation:
 To find the length of the ladder, we can use trigonometry and the given information.
First, let's draw a diagram to visualize the problem. The ladder forms a right triangle with the ground and the wall of the house. The angle between the ground and the ladder is 63 degrees.
Let's label the sides of the triangle:
- The length of the ladder is the hypotenuse (the side opposite the right angle).
- The height of the electric box on the wall is the opposite side (the side opposite the angle of 63 degrees).
- The distance from the base of the ladder to the wall is the adjacent side (the side adjacent to the angle of 63 degrees).
We know the height of the electric box is 31 feet, and the angle between the ground and the ladder is 63 degrees.
Using the sine function, we can set up the following equation:
sin(63 degrees) = opposite / hypotenuse
Plugging in the values, we get:
sin(63 degrees) = 31 / hypotenuse
Now, let's solve for the length of the ladder (hypotenuse).
Rearranging the equation, we have:
hypotenuse = 31 / sin(63 degrees)
Calculating this using a calculator, we find that the length of the ladder is approximately 34.43 feet.
Therefore, the length of the ladder is approximately 34.43 feet.
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