Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3
1 answer:
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Answer: 39.2
Check out the attached image
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Explanation:
Draw out the triangle or use the diagram provided by your teacher. It should look something similar to what I've attached.
Let m = length of side XZ
We are given that
angle Y = 75 degrees
angle Z = 67 degrees
which are the green angles shown in the diagram
Use the fact that the three angles (X,Y,Z) add to 180 degrees to find angle X
X+Y+Z = 180
X+75+67 = 180
X+142 = 180
X+142-142 = 180-142
X = 38
Now use the law of sines to find m
sin(X)/YZ = sin(Y)/XZ
sin(38)/25 = sin(75)/m
m*sin(38) = 25*sin(75)
m = 25*sin(75)/sin(38)
m = 39.22309 <<<--- make sure your calculator is in degree mode
m = 39.2
So XZ is roughly 39.2 feet in length
Check out the attached image
============================================================
Explanation:
Draw out the triangle or use the diagram provided by your teacher. It should look something similar to what I've attached.
Let m = length of side XZ
We are given that
angle Y = 75 degrees
angle Z = 67 degrees
which are the green angles shown in the diagram
Use the fact that the three angles (X,Y,Z) add to 180 degrees to find angle X
X+Y+Z = 180
X+75+67 = 180
X+142 = 180
X+142-142 = 180-142
X = 38
Now use the law of sines to find m
sin(X)/YZ = sin(Y)/XZ
sin(38)/25 = sin(75)/m
m*sin(38) = 25*sin(75)
m = 25*sin(75)/sin(38)
m = 39.22309 <<<--- make sure your calculator is in degree mode
m = 39.2
So XZ is roughly 39.2 feet in length
