Question

a portion of a hiking trail slopes upward at about a 6° angle. to the nearest tenth of a foot, what is the value of x, the hikers change in vertical position, if he has traveled a horizontal distance of 120 feet?
a. 8.7 ft
b. 12.6 ft
c. 20.0 ft
d. 23 ft

Explanation:

Step1: Identify trigonometric ratio

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{120}$

Step2: Solve for x

$x = 120 \times \tan(6^\circ)$

Step3: Calculate value

$\tan(6^\circ) \approx 0.1051$, so $x \approx 120 \times 0.1051 = 12.612$

Step4: Round to nearest tenth

$x \approx 12.6$

Answer:

B. 12.6 ft