Question

If sin (θ + 36°) = cos θ, where (θ + 36°) is acute, find θ.

Answer 1

Given: sin(θ + 36°) = cos θ, where (θ + 36°) is acute.

Step-wise calculation:

1. cos θ = sin(90° – θ), so sin(θ + 36°) = sin(90° – θ).

2. Since θ + 36° is acute and 90° – θ is acute, equate the angles:

θ + 36° = 90° – θ

3. Solve: 2θ = 54°

⇒ θ = 27°