Solve the problem.
-A straight trail with a uniform inclination of $13 ^ { \circ }$ leads from a lodge at an elevation of 900 feet to a mountain lake at an elevation of 8900 feet. What is the length of the trail (to the nearest foot)?
A) 35,563 feet
B) 39,564 feet
C) 8210 feet
D) 9134 feet

Question

Quizplus · Accepted Answer

The elevation change is 8900 - 900 = 8000 feet. To find the length of the trail, we use the formula for the length of the slope, which is the hypotenuse of a right triangle. The elevation change forms the opposite side of the triangle, and the angle of inclination is given as $13^\circ$. The formula derived from trigonometry is $\text{length} = \frac{\text{opposite}}{\sin(\theta)}$, where $\theta$ is the angle of inclination. Plugging in the values, we get $\text{length} = \frac{8000}{\sin(13^\circ)}$, which approximately equals 35,563 feet when calculated.

Solve the Problem 13∘13 ^ { \circ }13∘ Leads from a Lodge at an Elevation of 900 Feet

Solve the Problem $13 ^ { \circ }$ Leads from a Lodge at an Elevation of 900 Feet