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In triangle XYZ, we have angle X = 90 and tan Z = 3. What is cos Z?

 Aug 16, 2023

Best Answer 

 #4
avatar+130458 
+1

tan z  =   opp / adj  =  3 /  1

 

The hypotenuse =  sqrt [ 3^1 + 1^1 ] =  sqrt (10)

 

cos z  = adj / hyp  =    1 /sqrt (10)  =  sqrt (10) / 10

 

cool cool cool

 Aug 16, 2023
 #3
avatar+121 
+1

In a right triangle XYZ where angle X is 90 degrees, we can use the information provided to find the cosine of angle Z.

Given that tan Z = 3, we know that:

tanZ=oppositeadjacent=YZXZ=3.

Since triangle XYZ is a right triangle, we can use the Pythagorean theorem:

XY2+YZ2=XZ2.

Since angle X is 90 degrees, we have:

XZ2=XY2+YZ2=YZ2+YZ2=2YZ2.

Solving for YZ:

YZ2=XZ22.

Since we know the value of YZ/XZ (which is the tangent of angle Z):

tanZ=YZXZ=3.

Squaring both sides:

YZ2=9XZ2.

Now, substituting the value of YZ^2 from the Pythagorean theorem:

9XZ2=XZ22.

Solving for XZ:

XZ22=9XY2.

cosZ=12.

 Aug 16, 2023
 #4
avatar+130458 
+1
Best Answer

tan z  =   opp / adj  =  3 /  1

 

The hypotenuse =  sqrt [ 3^1 + 1^1 ] =  sqrt (10)

 

cos z  = adj / hyp  =    1 /sqrt (10)  =  sqrt (10) / 10

 

cool cool cool

CPhill Aug 16, 2023
 #5
avatar+52 
0

thanks!

newsss  Aug 16, 2023

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