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Find the value of tan W rounded to the nearest hundredth, if necessary.
W
V
41
40
U

Find The Value Of Tan W Rounded To The Nearest Hundredth If Necessary W V 41 40 U class=

Sagot :

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ WU^2=UV^2+WV^2\implies \sqrt{WU^2-UV^2}=WV \\\\\\ \sqrt{41^2-40^2}=WV\implies 9=WV[/tex]

Check the picture below.

View image Jdoe0001

The value of tan W rounded to the nearest hundredth, in the right angle triangle UVW is 4.55.

What is Pythagoras theorem?

Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.

The opposite side is the 40 units, while the hypotenuse side is 41 units long in the right angle triangle. Thus, the value of base side W is,

[tex](VW)^2+(40)^2=(41)^2\\(VW)=\sqrt{(41)^2-(40)^2}\\VW=9\rm\; units[/tex]

In the right angle triangle, the value of tan W is the ratio of side VW and UV. Thus,

[tex]\tan W=\dfrac{UV}{VW}\\\tan W=\dfrac{41}{9}\\\tan W=4.55[/tex]

Thus, the value of tan W rounded to the nearest hundredth, in the right angle triangle UVW is 4.55.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

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