Question

Solve for X Hello, I would appreciate any help given.

Answer 1

Step 1

Name all parameters

`\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{ = }(10)/(y) \\ \text{Cross multiply} \\ 0.6009y\text{ = 10} \\ y\text{ = }(10)/(0.6009) \\ y\text{ = 16.64} \\ \\ \sin 31\text{ = }(10)/(z) \\ 0.515\text{ = }(10)/(z) \\ \text{Cross multiply} \\ 0.515z\text{ = 10} \\ z\text{ = }(10)/(0.515) \\ z\text{ = 19.4} \end{gathered}`

Next, let find angle x.

`\begin{gathered} \text{For angle x,} \\ \text{Opposite = y} \\ \text{Hypotenuse = z} \\ \sin x\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \sin x\text{ = }(y)/(z) \\ \sin x\text{ = }(16.64)/(19.4) \\ \sin x\text{ = 0,85773} \\ x\text{ = }\sin ^(-1)0.85773x \\ x\text{ = 59} \end{gathered}`

Method 2

The Sum of angles in a triangle is 180 degrees

x + 31 + 90 = 180

x + 121 = 180

x = 180 - 121

x = 59