A 25 meter ladder is leaned against a tall building. If the ladder makes a 30 degree angle with the ground, how high up on the building (in meters) does the ladder fall?
h/25 = sin 30°
To find out how high up on the building the ladder falls, we can use trigonometry. In this case, we are given the length of the ladder (25 meters) and the angle it makes with the ground (30 degrees).
To determine the height on the building where the ladder falls, we need to find the vertical component of the ladder, which represents the height.
We can use the sine function to calculate the height. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the height represents the side opposite the 30-degree angle, and the hypotenuse is the length of the ladder. Using the formula, we have:
sin(30 degrees) = height / 25 meters
To solve for the height, we multiply both sides of the equation by 25 meters:
height = sin(30 degrees) * 25 meters
Calculating this expression, we find:
height ≈ 12.5 meters
Therefore, the ladder falls approximately 12.5 meters up on the building.