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-1(55/2640)
=tan-1(1/48)
Use your calculator to find the angle.
To find the tangent of the angle that the roadway makes with the horizontal, we need to use some trigonometry.
First, let's find the vertical height of the roadway. We are given that it rises 55ft.
Next, let's find the horizontal distance of the roadway. We are given that it is 1/2 mile, and we know that 1 mile is equal to 5280 feet. So, the horizontal distance is:
1/2 mile * 5280 ft/mile = 2640 ft.
Now, we can use the tangent function to find the angle:
tangent(angle) = vertical height / horizontal distance
tangent(angle) = 55 ft / 2640 ft
Now, we can divide both the numerator and the denominator by the greatest common divisor (GCD) to simplify the ratio:
GCD(55, 2640) = 5
55 / 5 = 11
2640 / 5 = 528
tangent(angle) = 11 / 528
So, the tangent of the angle that the roadway makes with the horizontal is 11 / 528.