Solution
Step 1:
Write all the trigonometric ratio for a right angle triangle
[tex]\begin{gathered} sin\theta\text{ = }\frac{opposite}{hypotenuse} \\ cos\theta=\frac{adjacent}{\text{hypotenuse}} \\ tan\theta=\frac{\text{oppos}\imaginaryI\text{te}}{adjacent} \end{gathered}[/tex]
Step 1:
Redraw the diagram and label all its sides.
The side facing the given angle is the opposite = ?
The side facing the right angle is the hypotenuse = 32
The third leg is the adjacent = x
Step3
The cosine ratio will be used to find the value of x since the given sides are adjacent and the hypotenuse.
[tex]\begin{gathered} cos\theta=\text{ }\frac{Adjacent}{Hypotenuse} \\ cos57\text{ = }\frac{x}{32} \\ 0.5446\text{ = }\frac{x}{32} \\ \text{x = 0.5446 }\times32 \\ x\text{ = 17.4} \end{gathered}[/tex]
Final answer
x = 17.4
