Question #194267

Two sides and an angles are given. Determine whether the given information results in one triangle, two triangles , or no triangle at all. If there is one or more triangles solve any triangle(s) that results. If there is no triangle, show and provide an explanation why.


B = 106 degrees, b = 5, a = 23


1
Expert's answer
2021-05-31T06:58:41-0400

Ans:- Given B=106, b=5, a=23B = 106 ^{\circ} ,\ b = 5, \ a = 23

We have using the Law of Sines....

SinAa=SinBb\Rightarrow \dfrac{SinA}{a}=\dfrac{SinB}{b}


SinA23=Sin1065\Rightarrow \dfrac{SinA}{23}=\dfrac{Sin106^{\circ}}{5}


So.........

Sin1(23×Sin1065)=A=Sin^{-1}(23\times\dfrac{Sin106^{\circ}}{5})=A= Undefined, outside the range of Sin functionSin\ function .

Therefore Angle A does not exist.


So There is no triangle exist of that type having parameters B=106, b=5, a=23B = 106 ^{\circ}, \ b = 5, \ a = 23


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