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In \(\triangle XYZ\), we have \(\angle X = 90^\circ\) and \(\tan Z = 3\). What is \(\cos Z\)?

Answer with an exact number

 Aug 6, 2020
 #1
avatar+21957 
+1

Since  tan  =  opposite / adjacent  --  If the tan(Z) = 3 = 3/1   

--->   opposite = 3  (or a multiple thereof)     and     adjacent = 1  (or the same multiple thereof)

 

This means that the hypotenuse is:  h2  =  32 + 12  =  10

--->   hypotenuse  =  sqrt(10)  (or the same multiple thereof)

 

cos(Z)  =  adjacent / hypotenuse  =  1 / sqrt(10) 

 Aug 6, 2020
 #2
avatar+169 
+1

I got the same thing!

\(\frac{1}{\sqrt{10}}\)

Nice work! I guess you have that many upvotes for a reason surpriseangel

Inspirational  Aug 6, 2020

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