Question

an engineer is designing a ski lift and has the following information about the angle of elevation. what is the angle of elevation from the top of the chair to the top of the triangle? round to the nearest degree.

Explanation:

Step1: Identify the sides for tangent

We know that in a right - triangle, if the opposite side to the angle of elevation is $y = 17.5$ ft and the adjacent side is $x = 25$ ft. The tangent of an angle $\theta$ in a right - triangle is given by $\tan\theta=\frac{y}{x}$.

Step2: Calculate the tangent value

Substitute $y = 17.5$ and $x = 25$ into the tangent formula: $\tan\theta=\frac{17.5}{25}=0.7$.

Step3: Find the angle

To find the angle $\theta$, we use the inverse - tangent function, $\theta=\arctan(0.7)$. Using a calculator, $\theta=\arctan(0.7)\approx35^{\circ}$.

Answer:

$35$