Answer:
To find the length of side YZ in triangle XYZ, we can use the Law of Sines. The Law of Sines states:
\[\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\]
Given that XY = 7 cm, angle X = 55 degrees, and angle Z = 80 degrees, we need to find the length of side YZ.
First, let's find angle Y:
Angle Y = 180 - angle X - angle Z
Angle Y = 180 - 55 - 80
Angle Y = 45 degrees
Now, we can use the Law of Sines to find the length of side YZ:
\[\frac{YZ}{\sin 55} = \frac{7}{\sin 45}\]
\[YZ = \frac{7 \times \sin 55}{\sin 45}\]
\[YZ \approx \frac{7 \times 0.8192}{0.7071}\]
\[YZ \approx \frac{5.735}{0.7071}\]
\[YZ \approx 8.11 \, \text{cm}\]
Therefore, the length of side YZ in triangle XYZ is approximately 8.11 cm.
