Solution:
Given the ΔABC below:
To find the missing side,
Step 1: Identify the sides of the triangle.
Thus,
[tex]\begin{gathered} hypotenuse\Rightarrow AB(longest\text{ side of the triangle\rparen} \\ opposite\Rightarrow AC(side\text{ facing the angle\rparen} \\ adjacent\Rightarrow BC \end{gathered}[/tex]
Step 2: Evaluate the value of x, using trigonometric ratios.
From trigonometric ratios,
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]
where
[tex]\theta=\angle B[/tex]
Thus,
[tex]\begin{gathered} \cos B=\frac{adjacent}{hypotenuse} \\ =\frac{BC}{AB} \\ \Rightarrow\cos B=\frac{x}{28} \\ cross-multiply, \\ x=28\times\cos B \\ but\text{ B=59} \\ \Rightarrow x=28\times\cos59 \\ =28\times0.5150380749 \\ =14.4210661 \\ \Rightarrow x\approx14.4 \end{gathered}[/tex]
Hence, the value of x, to the nearest tenth, is
[tex]14.4[/tex]
