A highway makes an angle of 6 with the horizontal.This angle is maintained for a horizontal distance of 5 miles.To the nearest hundredth of a mile, how high does the highway rise in this 5- mile section?Show the steps you use to find the distance.

Draw a diagram

tan 6° = d/5
d = 0.53 mi

Using

A forest ranger spots a fire from a 28-foot tower. The angle of depression from the tower to the fire is 11 .


To the nearest foot, how far is the fire from the base of the tower? Show the steps you use to find the solution.

To find the height that the highway rises in a 5-mile section, we need to use trigonometry. In this case, we have the angle of elevation as 6 degrees and the horizontal distance traveled as 5 miles.

Step 1: Convert the angle from degrees to radians.
To use trigonometry functions like sine or cosine, we need to convert the angle from degrees to radians. Since there are π radians in 180 degrees, we can convert 6 degrees to radians using the following equation:

angle_radians = angle_degrees * (π / 180)
angle_radians = 6 * (π / 180)
angle_radians ≈ 0.10472 radians

Step 2: Determine the height using the tangent function.
The tangent function relates the height (opposite side) to the distance (adjacent side) for a given angle. For this problem, we can use the tangent function to find the height.

height = distance * tangent(angle_radians)
height = 5 * tangent(0.10472)
height ≈ 0.90905 miles

Therefore, the highway rises approximately 0.90905 miles or 0.91 miles (rounded to the nearest hundredth) in this 5-mile section.