Question

In the figure below ABC- XZY

find cosZ, sin Z, tan Z

round your answer to the nearest hundredth

Answer 1

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.