To determine how far up the wall the ladder reaches, we can use trigonometric functions. In this case, the angle between the ladder and the ground is 60 degrees.
Let's assume that the distance the ladder reaches up the wall is represented by the variable "x." The ladder, the wall, and the ground form a right-angled triangle, where the ladder is the hypotenuse.
In a right-angled triangle, the trigonometric function used to relate the lengths of the sides to the angles is the sine function. Specifically, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
So, we can use the sine function to solve this problem. The sine of 60 degrees is equal to the length of the side opposite the angle (x) divided by the length of the hypotenuse (6 meters):
sin(60°) = x / 6
The sine of 60 degrees is equal to √3 / 2, so we can substitute that value into the equation:
√3 / 2 = x / 6
To solve for x, we can multiply both sides of the equation by 6:
6 * (√3 / 2) = x
Simplifying the expression on the left side:
3√3 = x
Therefore, the ladder reaches approximately 3√3 meters up the wall.