A roadway rises 55ft in horizontal distance of 1/2 mile (1mile=5280ft) Find the tangent of the angle that it makes with the horizontal.
tan = rise/run = 55/2640 = 1/48
Well, if we look at this situation from an angle... pun absolutely intended... we can consider the rise and the run of the roadway.
The rise of the roadway is 55 feet, and the horizontal distance is 1/2 mile. Now, let's convert that 1/2 mile to feet. Since 1 mile is equal to 5280 feet, 1/2 mile would be 5280 divided by 2, which is 2640 feet.
So, we have a rise of 55 feet and a run of 2640 feet. To find the tangent of the angle, we just need to divide the rise by the run.
Now, here comes the funny part... Tan(gent) is actually the rise divided by the run, but in this case, it's not a tangent running for office. So, let's calculate this:
Tangent(angle) = rise / run
Tangent(angle) = 55 feet / 2640 feet
Dividing these numbers gives us a funn- I mean, the tangent of the angle that the roadway makes with the horizontal. Go ahead, calculate it!
To find the tangent of the angle that the roadway makes with the horizontal, we can use trigonometry.
The given information is that the roadway rises 55ft in a horizontal distance of 1/2 mile. To find the angle, we can use the tangent function:
tangent(angle) = opposite/adjacent
Here, the opposite side is the rise (55ft) and the adjacent side is the horizontal distance (1/2 mile or 1/2 * 5280ft = 2640ft).
Plugging in these values, we have:
tangent(angle) = 55ft/2640ft
Now, let's calculate the tangent of the angle:
tangent(angle) = 0.0208333
Therefore, the tangent of the angle that the roadway makes with the horizontal is approximately 0.0208333.
To find the tangent of the angle, we can use the relationship between the height (rise) and the horizontal distance.
First, we need to convert the given horizontal distance of 1/2 mile to feet. We have:
1 mile = 5280 feet
Therefore, 1/2 mile = (1/2) * 5280 feet = 2640 feet
Now, we can use the given rise of 55 feet and the horizontal distance of 2640 feet to find the tangent of the angle. The tangent of an angle can be defined as the ratio of the rise to the horizontal distance.
Tangent (θ) = (rise / horizontal distance)
Tangent (θ) = (55 feet / 2640 feet)
Tangent (θ) ≈ 0.0208
So, the tangent of the angle is approximately 0.0208.