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9514 1404 393
Answer:
C) 14 cm
Step-by-step explanation:
A triangle solver can quickly show you the third side is 14 cm.
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The law of cosines can be used for this purpose. If the given sides are 'a' and 'b', and the third side is 'c', then that law tells you ...
c² = a² +b² -2ab·cos(C)
c² = 7² +11² -2·7·11·cos(100°) ≈ 196.74
c ≈ √196.74 ≈ 14.03
The length of the third side is about 14 cm.
Because the two angles on the right add to 180 degrees, we can create this system:
We can also prove that
, which, when solved, shows that 
.
When plugged in to the original equation, we find that y = 105 degrees.
We can also prove that
When plugged in to the original equation, we find that y = 105 degrees.