Given:
A figure of a right triangle.
To find:
The missing side by using the trigonometric ratios.
Solution:
In a right angle triangle,
[tex]\cos \theta=\dfrac{Adjacent}{Hypotenuse}[/tex]
In triangle ABC,
[tex]\cos A=\dfrac{AC}{AB}[/tex]
[tex]\cos (31^\circ)=\dfrac{b}{270}[/tex]
[tex]0.857=\dfrac{b}{270}[/tex]
Multiply both sides by 270.
[tex]0.857\times 270=b[/tex]
[tex]231.39=b[/tex]
[tex]b\approx 231.4[/tex]
Therefore, the missing side length is b=231.4 inches.
