A bobsled is on an inclined sheet of ice that is frictionless. What must be the angle of the incline if the acceleration of the bobsled is 2.77m/s^2?

 θ = 73.6º

Explanation:

To solve this exercise, let's use Newton's second law. Let's set a reference system where the x-axis is parallel to the inclined plane

with trigonometry we can find the components of the weight

           sin θ = Wₓ / W

           cos θ= W_y / W

           Wₓ = W sin θ

           W_ = W cos θ

Y axis  

           N - W_y = 0

           N = W_y

X axis

           Wₓ - fr = m a

            mg cos θ - fr = m a

indicate that friction is zero, fr = 0

            cos θ = a / g

            θ = cos⁻¹  

let's calculate

            θ = cos⁻¹  

            θ = 73.6º