Explain why there is no triangle that has sides of lengths a = 2 inches, b = 11

Question

Explain why there is no triangle that has sides of lengths a = 2 inches, b = 11 inches, and c = 3 inches. The Pythagorean Theorem is a special case of the Law of Cosines. Explain. To solve a triangle in which the lengths of the three sides are given (SSS), a mathematics professor recommends the following procedure. Use the Law of Cosines to find the measure of the largest angle. Use the Law of Sines to find the measure of a second angle. Find the measure of the third angle by using the formula A + B + C = 180 degree. Explain why this procedure is easier than using the Law of Cosines to find the measure of all three angles. Explain why the Law of Cosines cannot be used to solve a triangle in which you are given the measures of two angles and the length of the included side (ASA). In Exercise 1 to 52, round answers according to the rounding conventions on page 140. In Exercises 1 to 14, find the third side of the triangle. a = 12, b = 18, C = 44 degree b = 30, c = 24, A = 120 degree a = 120, c = 180, B = 56 degree a = 400, b = 620, c = 116 degree b = 60, c = 84, A = 13 degree a = 122, c = 144, B = 48 degree a = 9.0, c = 7.0, C = 72 degree b = 12, c = 22, A = 55 degree a = 4.6, b = 7.2, C = 124 degree b = 12.3, c = 14.5, A = 6.5 degree a = 25.9, c = 33.4, B = 84.0 degree a = 14.2, b = 9.30, C = 9.20 degree a = 122, c = 55.9, B = 44.2 degree b = 444.8, c = 389.6, A = 78.44 degree In Exercise 15 to 24, given three sides of a triangle, find the specified angle. a = 25, b = 32, c = 40; find A. a = 60, b = 88, c = 120; find B. a = 80, b = 90, c = 12; find C. a = 108, b = 132, c = 160; find A. a = 80.0, b = 92.0, c = 124; find B. a = 166, b = 124, c = 139; find B. a = 1025, b = 6250, c = 1420; find C. a = 4.7, b = 3.2, c = 5.9; find A. a = 32.5, b = 40.1, c = 29.6; find B. a = 112.4, b = 96.80, c = 129.2; find C.

Explanation / Answer

1)
a = 12 , b = 18 , C = 44
We need to find side, c
c^2 = a ^2 + b^2 - 2abcosC
c^2 = 12^2 + 18^2 - 2(12)(18)cos(44)
c^2 = 157.245206253552
c = 12.539745063339685
Rounding, we get c = 13 ---> ANSWER

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3)
a = 120 , c = 180 and B = 56
b^2 = a^2 + c^2 - 2accosB
b^2 = 120^2 + 180^2 - 2*120*180*cos(56)
b^2 = 22642.8665700528
b = 150.4754683330568671
Rounding, b = 150 ---> ANSWER

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5)
b = 60 , c = 84 , A = 13
a^2 = b^2 + c^2 - 2bccosA
a^2 = 60^2 + 84^2 - 2*60*84*cos(13)
a^2 = 834.3497469672
a = 29 ---> ANSWER

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7)
a = 9 , b = 7 and C = 72
c^2 = a^2 + b^2 - 2abcosC
c^2 = 9^2 + 7^2 - 2*9*7*cos(72)
c^2 = 91.06385870875
c = 9.5427385329762651
c = 9.5 --> ANSWER

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9)
a = 4.6 , b = 7.2 and C = 124
c^2 = a^2 + b^2 - 2abcosC
c^2 = 4.6^2 + 7.2^2 - 2*4.6*7.2*cos(124)
c^2 = 110.04093792591904
c = 10.49003993919561014
c = 10 ----> ANSWER

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