Solution
Step 1
Write the given data
[tex]\begin{gathered} \text{X = 47}^o \\ Z\text{ = 50}^o \\ \text{y = 52.6cm} \end{gathered}[/tex]
Step 2:
To find side x, find angle Y, using the sum of angles i a triangl theorem.
[tex]\begin{gathered} Sum\text{ of angles in a triangle = 180} \\ X\text{ + Y + Z = 180} \\ \text{47 + Y + 50 = 180} \\ Y\text{ = 180 - 97} \\ \text{Y = 83}^o \end{gathered}[/tex]
Step 3:
Next, use the sine rule to find side x.
[tex]\begin{gathered} \frac{x}{sinX}\text{ = }\frac{y}{sinY} \\ \frac{x}{sin47}\text{ = }\frac{52.6}{sin83} \\ \frac{x}{0.73135}\text{ = }\frac{52.6}{0.992546} \\ \text{x = }\frac{0.73135\times52.6}{0.992546} \\ \text{ x = 38.8 cm} \end{gathered}[/tex]
Final answer
x = 38.8 cm
