Answer:
The measure of the angle the cable car track makes with the valley floor = 0.66 rad = 37.95°
Step-by-step explanation:
Let the angle the cable car makes with the valley floor be θ
Let the height of the community on top of the overlooking bluff be y
Let the horizontal distance along the valley floor from the base of the incline to the foot of bottom of the height that contains the community be x
An image of this is presented in the attached file to this solution.
The grade of the Monongahela Incline is given as 78% = 0.78
This means that
(y-0)/(x-0) = 0.78
(y/x) = 0.78
Since, this setup forms a right angle triangle,
Using trigonometric relations,
Tan θ = (Opp/Adj)
Opp = y
Adj = x
(Opp/Adj) = (y/x) = 0.78
Tan θ = 0.78
θ = tan⁻¹ (0.78) = 0.6624 rad = 0.66 rad = 37.95°
Hope this Helps!!!
