Based on the right-angled triangle shown above, the measure of the indicated angle to the nearest degree is 24 degree.
In order to determine the trigonometric ratio for cosθ, we would have to apply the basic cosine trigonometric function because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle;
cos(θ) = Adj/Hyp
Where:
- Adj represent the adjacent side of a right-angled triangle.
- Hyp represent the hypotenuse of a right-angled triangle.
- θ represent the angle.
By applying the cosine trigonometric function ratio to this right-angled triangle, we have the following:
cosθ = adjacent side/hypotenuse
cosθ = 55/60
Angle, θ = 23.5565 ≈ 24 degree.