Answer:
x = 23.5
Step-by-step explanation:
In right triangle UVW, we have been given the measure of the angle at vertex W along with the length of the side adjacent to this angle (VW) and the length of the side opposite this angle (UV).
To find the value of x, we can use the tangent trigonometric ratio:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Sine trigonometric ratio}}\\\\\sf \sin(\theta)=\dfrac{O}{H}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{O is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{H is the hypotenuse (the side opposite the right angle).}\end{array}}[/tex]
In this case:
- θ = W = 71°
- O = UV = x
- A = VW = 8.1
Substitute the values into the tangent ratio and solve for x:
[tex]\tan 71^{\circ}=\dfrac{x}{8.1} \\\\\\ x=8.1 \tan 71^{\circ} \\\\\\ x=23.52410810917... \\\\\\ x=23.5\; \sf (nearest\;tenth)[/tex]
Therefore, the value of x rounded to the nearest tenth is:
[tex]\LARGE\boxed{\boxed{x=23.5}}[/tex]
