A road rises 140 feet per horizontal mile. What angle does the road make with the horizontal?
Draw a triangle.
The the road would be the base, which is 1 mile or 5280 feet and the side opposite angle A would be 140.
You need angle A. You have side a = 140 feet, and side b = 5280 feet.
tan A = opp/adj = a/b = 140/5280
tan A = 140/5280 = ?
arctan ? = angle A
To find the angle that the road makes with the horizontal, we can use trigonometry. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the rise of 140 feet and the adjacent side is the horizontal distance of 1 mile (5280 feet).
So, the tangent of the angle can be calculated as:
Tangent of angle = rise / horizontal distance
Tangent of angle = 140 feet / 5280 feet
Dividing 140 by 5280, we get:
Tangent of angle = 0.0265151515
Now, we need to find the angle whose tangent is equal to 0.0265151515. To do this, we can use the inverse tangent function (also known as arctan or tan^-1) on a calculator:
angle = arctan(0.0265151515)
angle ≈ 1.518 degrees
Therefore, the road makes an angle of approximately 1.518 degrees with the horizontal.
To find the angle that the road makes with the horizontal, you can use trigonometry. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the opposite side is the rise of the road, which is 140 feet, and the adjacent side is the horizontal distance of one mile, which is 5,280 feet.
So, the tangent of the angle is 140/5280. To find the angle itself, we can take the inverse tangent (also known as the arctan) of this ratio.
Using a calculator or a math software, you can find that the inverse tangent of 140/5280 is approximately 1.518°.
Therefore, the road makes an angle of approximately 1.518° with the horizontal.