What is the value of θ for the acute angle in a right triangle?

sin (θ) = cos (58°)

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Well, since the problem is talking about a right triangle, and one measurement is given, you can solve for the other one by simply subtracting 58 from 90.

so sin (theta) = cos 90 - 58

sin (32) = cos 58

To determine the value of θ in a right triangle and given this condition, we can solve for θ from the given:

sin (θ) = cos (58°)

sin θ = 0.5299

sin-1 (0.5299) = θ

θ = 32 degrees

Therefore, the acute angle measures 32 degrees.