Answer to Question #194267 in Trigonometry for Bill

Question

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

Answer 1

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

We have using the Law of Sines....

$\Rightarrow \dfrac{SinA}{a}=\dfrac{SinB}{b}$

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

So.........

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

Therefore Angle A does not exist.

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