Respuesta :

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

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