A 5 m stepladder propped against a classroom wall forms an angle of 30 degree with the wall. Exactly how far is the top of the ladder from the floor? Express your answer in radical form. What assumption did you make?
To find the exact distance between the top of the ladder and the floor, we can use trigonometry. In this case, we can use the sine function to find the length of the ladder.
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this scenario, the hypotenuse represents the length of the ladder, and the opposite side represents the distance between the top of the ladder and the floor.
Let's assume that the distance between the top of the ladder and the floor is represented by the variable "x".
Using the sine function, we can set up the following equation:
sin(30°) = x / 5
Now we can solve for "x". First, we need to determine the exact value of sin(30°). The sine of 30 degrees is 1/2.
Substituting this into the equation:
1/2 = x / 5
Next, we can solve for "x" by multiplying both sides of the equation by 5:
5 * (1/2) = x
2.5 = x
Therefore, the top of the ladder is approximately 2.5 meters from the floor.
Now, let's address the assumption made in this calculation. It is assumed that the ladder is leaning against the wall in a straight line, forming a right triangle with the floor. Additionally, we assume that the ladder does not slip or have any external forces acting on it that would affect its position. These assumptions are commonly made when using trigonometry to solve similar problems.