Two sides and an angle are given below. Determine whether the given information

Question

Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. b=8, c=7, B=140 degrees.

Multiple Choice/Fill in the Blank

A. A single triangle is produced where C=___ degrees, A=___ degrees, and a=___.

B.Two triangles are produced, where the triangle with the smaller angle C has C_1=___degrees , A_1=___ degrees and a_1=___, and the triangle with the larger angle C has C_2=___ degrees, A_2=___ and a_=___.

C. No triangles are produced.

Explanation / Answer

b=8,c=7, B=140

Using sine law

sin B/b = sin C/c

sin140 / 8=sin C /7

C = 34.225 degree

A = 180-B-C= 5.775 degree

sin B/b= sin A/a

sin 140/8= sin 5.78/a

a = 1.252

Correct option is A

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