A fire ladder extends 18m. Each storey of a burning building is 10ft. If the ladder can have a maximum angle with the ground of 75 degrees, to what storey would the ladder reach?
sin(75) = 18/x
x = 18/sin(75)
x = 61.14 ft
approx. the 6th story
you need to convert 18 m to ft btw or 10ft to meters
thanks
To determine the storey at which the ladder would reach, we need to convert the measurements to the same unit. Since the ladder's length and the height of each storey are given in different units (meters and feet), we need to convert one of them.
Let's convert the height of each storey from feet to meters for consistency.
1 foot is approximately equal to 0.3048 meters.
Since each storey is 10 feet, we can calculate the height in meters by multiplying 10 by 0.3048, which is approximately equal to 3.048 meters.
Now we have a ladder length of 18 meters and a storey height of 3.048 meters.
To determine the storey at which the ladder would reach, we can consider the maximum angle of 75 degrees.
Since the ladder forms a right triangle with the ground (assuming the building is vertical), the ladder's length is the hypotenuse of the triangle, and the height of each storey is the opposite side.
Using trigonometry, we can find the length of the adjacent side of the triangle, which represents the horizontal distance covered by the ladder.
In this case, we have the hypotenuse (18 meters) and the angle (75 degrees), and we want to find the adjacent side.
We can use the cosine of the angle to calculate the adjacent side:
adjacent side = hypotenuse * cosine(angle)
adjacent side = 18 * cos(75°)
Using a calculator, the calculation gives us an adjacent side length of approximately 4.2537 meters.
Since each storey has a height of 3.048 meters, we can determine how many storeys the ladder can reach by dividing the adjacent side length by the storey height:
number of storeys = adjacent side length / storey height
number of storeys = 4.2537 / 3.048
Calculating this, we find that the ladder would reach approximately 1.394 storeys.
Therefore, the ladder would reach about 1.394 storeys.
Since we cannot have a fraction of a storey, the ladder would reach the nearest whole storey, which is the first storey.