The magnitude of angle Z include the following:
cosZ = 0.471
sinZ = 0.88
tanZ = 1.875
How to calculate the magnitude of angle Z?
In order to determine the magnitude of angle Z, we would apply the basic trigonometric ratio because the given side lengths represent the adjacent side, opposite side, and hypotenuse of a right-angled triangle.
cos(θ) = Adj/Hyp
Where:
- Adj represents the adjacent side of a right-angled triangle.
- Hyp represents the hypotenuse of a right-angled triangle.
- θ represents the angle.
For cosZ, we would apply the cosine trigonometric ratio as follows;
cosZ = 13.6/28.9
cosZ = 0.4706
Z = cos⁻¹(0.4706)
Z = 61.93°.
For sinZ, we would apply the sine trigonometric ratio as follows;
sinZ = 25.5/28.9
sinZ = 0.8824
Z = sin⁻¹(0.8824)
Z = 118.07.
For tanZ, we would apply the sine trigonometric ratio as follows;
tanZ = 25.5/13.6
tanZ = 1.875
Z = tan⁻¹(1.875)
Z = 61.93.