Step 1
Name all parameters
[tex]\begin{gathered} \text{for }\theta\text{ = 31} \\ \text{Opposite = 10} \\ \text{Hypotenuse = z} \\ \text{Adjacent = y} \\ \text{Tan 31 = }\frac{Opposite}{\text{Adjacent}} \\ 0.6009\text{ = }\frac{10}{y} \\ \text{Cross multiply} \\ 0.6009y\text{ = 10} \\ y\text{ = }\frac{10}{0.6009} \\ y\text{ = 16.64} \\ \\ \sin 31\text{ = }\frac{10}{z} \\ 0.515\text{ = }\frac{10}{z} \\ \text{Cross multiply} \\ 0.515z\text{ = 10} \\ z\text{ = }\frac{10}{0.515} \\ z\text{ = 19.4} \end{gathered}[/tex]
Next, let find angle x.
[tex]\begin{gathered} \text{For angle x,} \\ \text{Opposite = y} \\ \text{Hypotenuse = z} \\ \sin x\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \sin x\text{ = }\frac{y}{z} \\ \sin x\text{ = }\frac{16.64}{19.4} \\ \sin x\text{ = 0,85773} \\ x\text{ = }\sin ^{-1}0.85773x \\ x\text{ = 59} \end{gathered}[/tex]
Method 2
The Sum of angles in a triangle is 180 degrees
x + 31 + 90 = 180
x + 121 = 180
x = 180 - 121
x = 59
