A certain part of a hiking trail slopes upward at about 10° angle. After traveling a horizontal distance of 120ft along this part of the trail. What would be the change in hiker's vertical position? What distance has the hiker traveled along the path?

Review your basic trig functions:

the vertical height is

y/120 = tan10°

the distance walked is

z/120 = sec10°

To find the change in the hiker's vertical position and the distance traveled along the path, we can use trigonometry.

The change in the hiker's vertical position can be determined using the sine function. The formula to find the change in vertical position (h) is given by the formula:

h = d * sin(theta)

Where:
h = change in vertical position
d = horizontal distance traveled
theta = angle of inclination

Given:
d = 120 ft (horizontal distance)
theta = 10° (angle of inclination)

Substituting the values into the formula, we have:

h = 120 * sin(10°)

Calculating this, we find:

h ≈ 120 * 0.1736
h ≈ 20.832 ft

Therefore, the change in the hiker's vertical position is approximately 20.832 ft.

To find the distance traveled along the path, we can use the cosine function. The formula to find the distance traveled (s) is given by the formula:

s = d * cos(theta)

Where:
s = distance traveled

Using the same values we have:

s = 120 * cos(10°)

Calculating this, we find:

s ≈ 120 * 0.9848
s ≈ 118.176 ft

Therefore, the distance traveled along the path is approximately 118.176 ft.