Near Pittsburgh, a cable car transports people from the Monongahela River valley to the community on top of the overlooking bluff. The Monongahela Incline has a grade of 78%. Find the measure of the angle the cable car track makes with the valley floor. If necessary, round to the nearest hundredth

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°

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step-by-step explanation: