Question

19) Find side xX = 47°, Z =50°, y = 52.6 cm

Answer 1

Step 1

Write the given data

`\begin{gathered} \text{X = 47}^o \\ Z\text{ = 50}^o \\ \text{y = 52.6cm} \end{gathered}`

Step 2:

To find side x, find angle Y, using the sum of angles i a triangl theorem.

`\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}`

Step 3:

Next, use the sine rule to find side x.

`\begin{gathered} (x)/(sinX)\text{ = }(y)/(sinY) \\ (x)/(sin47)\text{ = }(52.6)/(sin83) \\ (x)/(0.73135)\text{ = }(52.6)/(0.992546) \\ \text{x = }(0.73135*52.6)/(0.992546) \\ \text{ x = 38.8 cm} \end{gathered}`

Final answer

x = 38.8 cm