How many sides does the polygon have ?
1 answer:
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Answer:
There is only one triangle possible
Angles:
A = 112, B = 31.9932, C = 36.0068
Sides:
a = 7, b = 4, c = 4.4384
See the attached image for a visual diagram.
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Explanation:
Use the law of sines to solve for angle B
sin(A)/a = sin(B)/b
sin(112)/7 = sin(B)/4
0.132454836366684 = sin(B)/4
4*0.132454836366684 = 4*sin(B)/4
0.529819345466736 = sin(B)
sin(B) = 0.529819345466736
arcsin(sin(B)) = arcsin(0.529819345466736)
B = arcsin(0.529819345466736) ... or ... B = 180 - arcsin(0.529819345466736)
B = 31.9932495421859 ... or ... B = 148.006750457814
B = 31.9932 ... or ... B = 148.0068
If B = 31.9932, then C = 180-A-B = 180-112-31.9932 = 36.0068
If B = 148.0068, then C = 180-A-B = 180-112-148.0068 = -80.0068
A negative angle is not possible, so we toss out this value
So only angle B = 31.9932 is possible
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Once we know the measure of angle C, we can use that to find side c by using the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = (7)^2 + (4)^2 - 2*(7)*(4)*cos(36.0068)
c^2 = 49 + 16 - 56*0.808947228919362
c^2 = 49 + 16 - 45.3010448194843
c^2 = 19.6989551805157
c = sqrt(19.6989551805157)
c = 4.4383505022154
c = 4.4384
By this point, we're done since we found the remaining missing angles and missing side.
There is only one triangle possible
Angles:
A = 112, B = 31.9932, C = 36.0068
Sides:
a = 7, b = 4, c = 4.4384
See the attached image for a visual diagram.
==============================================
Explanation:
Use the law of sines to solve for angle B
sin(A)/a = sin(B)/b
sin(112)/7 = sin(B)/4
0.132454836366684 = sin(B)/4
4*0.132454836366684 = 4*sin(B)/4
0.529819345466736 = sin(B)
sin(B) = 0.529819345466736
arcsin(sin(B)) = arcsin(0.529819345466736)
B = arcsin(0.529819345466736) ... or ... B = 180 - arcsin(0.529819345466736)
B = 31.9932495421859 ... or ... B = 148.006750457814
B = 31.9932 ... or ... B = 148.0068
If B = 31.9932, then C = 180-A-B = 180-112-31.9932 = 36.0068
If B = 148.0068, then C = 180-A-B = 180-112-148.0068 = -80.0068
A negative angle is not possible, so we toss out this value
So only angle B = 31.9932 is possible
--------------------------
Once we know the measure of angle C, we can use that to find side c by using the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = (7)^2 + (4)^2 - 2*(7)*(4)*cos(36.0068)
c^2 = 49 + 16 - 56*0.808947228919362
c^2 = 49 + 16 - 45.3010448194843
c^2 = 19.6989551805157
c = sqrt(19.6989551805157)
c = 4.4383505022154
c = 4.4384
By this point, we're done since we found the remaining missing angles and missing side.
Answer:
C. If the probability of an event occurring is 1.5, then it is certain that the event will occur.
Step-by-step explanation:
Probability is a value between <em>0 and 1</em> (including both values). Thus, to say that there is a probability of 1.5 is not correct, and, therefore, this statement is not true.
We can rewrite the statement as "If the probability of an event occurring is 1, then it is completely certain that the event will occur."
Statement A.
Suppose the event is A. Then, if P(A) = 0, it is completely certain that the event will not occur. It is true.
Statement B.
. Then, the statement is true.
Statement C.
We already explained the <em>statement C is not true</em> because the values for probabilities are between 0 and 1 (including both values). A probability of 1.5 is meaningless as a result.
Statement D.
For the same reason explained in C, the probability can never be a negative value. So, this statement is also true.