Find the number of distinct triangles with the measurements a=5, b=2, and A=51
+128407 Since we have a SSA situation, we could have more than one triangle ...Using the Law of Sines, we have......
sin B / 2 = sin 51 / 5 ...... so......
sin-1 ((2/5)* sin 51) = about 18.11º = angle B
And......subtracting this from 180 we have (180 - 18.11)° = 161.89º.......but....this angle added to the known angle of 51° is greater than 180°, so only one triangle is possible.......as Melody found......
The angles are
A = 51 B = 18.11 C = 110.89
And side c = c / sin 110.89 = 5 /sin 51 ...so.... c = 5(sin110.89) / sin 51 = about 6.01
So the sides are a = 5, b = 2 and c = 6.01
+118608 Find the number of distinct triangles with the measurements a=5, b=2, and A=51
There appears to only be one.
+33614 Depends what is meant by "distinct" I guess. If you reflect Melody's triangle in any of its sides, you get another one that can't be rotated into the first.
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+118608 Hi Alan,
It would still be congrent though.
You could translate it too then it would be in a different position so it would not be the same triangle. :)
+128407 Since we have a SSA situation, we could have more than one triangle ...Using the Law of Sines, we have......
sin B / 2 = sin 51 / 5 ...... so......
sin-1 ((2/5)* sin 51) = about 18.11º = angle B
And......subtracting this from 180 we have (180 - 18.11)° = 161.89º.......but....this angle added to the known angle of 51° is greater than 180°, so only one triangle is possible.......as Melody found......
The angles are
A = 51 B = 18.11 C = 110.89
And side c = c / sin 110.89 = 5 /sin 51 ...so.... c = 5(sin110.89) / sin 51 = about 6.01
So the sides are a = 5, b = 2 and c = 6.01
