Answer:
3.43
Step-by-step explanation:
The tangent ratio is the ratio of the length of the side opposite an angle in a right triangle to the length of the adjacent side:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Tangent trigonometric ratio}}\\\\\sf \tan(\theta)=\dfrac{O}{A}\\\\\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{$A$ is the side adjacent the angle.}\end{array}}[/tex]
To find the value of tan(Y), we first need to find the length of the side opposite angle Y in the given right triangle WXY. To do this, we can use the Pythagorean Theorem:
[tex]WX^2+XY^2=WY^2\\\\x^2+14^2=50^2\\\\x^2+196=2500\\\\x^2=2304\\\\x=\sqrt{2304}\\\\x=48[/tex]
Now we have found the length of the side opposite angle Y, we can plug this and the length of the side adjacent angle Y into the tangent ratio:
[tex]\tan Y = \dfrac{48}{14}\\\\\\\tan Y=3.4285714285714...[/tex]
To round 3.4285714285714 to the nearest hundredth, look at the digit in the thousandths place, which is 8. Since 8 is greater than or equal to 5, we round up the hundredths place. Therefore, the number rounded to the nearest hundredth is 3.43.
So, the value of tan Y rounded to the nearest hundredth is:
[tex]\LARGE\boxed{\boxed{\tan Y=3.43}}[/tex]
