For problems 1, 2, and 4, check out this link
https://brainly.com/question/27021415
as they were answered there earlier.
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Problem 3
Answer: Not possible to solve
A triangle cannot be constructed with these parameters.
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Explanation:
Use the Law of Sines to find angle B
sin(A)/a = sin(B)/b
sin(120)/12 = sin(B)/13
sin(B) = 13*sin(120)/12
sin(B) = 0.93819419
B = arcsin(0.93819419) or B = 180 - arcsin(0.93819419)
B = 69.75047247 or B = 180 - 69.75047247
B = 69.75047247 or B = 110.24952753
These angle values are approximate.
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If B = 69.75047247, then,
A+B+C = 180
C = 180 - (A+B)
C = 180 - (120 + 69.75047247)
C = -9.75047247000001
We get a negative result which isn't valid.
This means B = 69.75047247 isn't valid either.
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If B = 110.24952753, then,
A+B+C = 180
C = 180 - (A+B)
C = 180 - (120 + 110.24952753)
C = -50.24952753
We get a similar conclusion here as well.
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No matter what value of B we go with, we end up with a negative value for angle C.
Negative angles are not allowed.
Therefore, we cannot construct a triangle with sides a = 12, b = 13 and angleA = 120 degrees.
This is one example of an SSA triangle leading to no possible solutions. Refer to the SSA ambiguous case for more info.
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Check out the diagram below. Imagine that point B can be anywhere on the dotted circle. Imagine it can rotate around as in an animation. This circle is centered at point C and has radius a = 12. No matter where point B is placed, we cannot get it to land on the horizontal line to therefore form a triangle. Simply put: side a = 12 is too short.
I used GeoGebra to make the diagram and make sure it's to scale. This is to visually verify that we cannot construct such a triangle with these parameters.
