Question

QuestionThe unknown triangle ABC has angle A = 56° and sides a = 32 and c = 34. How many solutions are there for triangleABC? if there are infinitely many, enter oo.

Answer 1

The law of sines is a theorem for triangle which states that for a triangle with sides a,b,c and angle A,B,C

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

Where,

a=32

A=56

c=34

`\begin{gathered} (32)/(\sin56)=(b)/(\sin B)=(34)/(\sin C) \\ (32)/(\sin56)=(34)/(\sin C) \\ \sin C=(34*\sin 56)/(32) \\ \sin C=0.881 \end{gathered}`
`\begin{gathered} (b)/(\sin B)=38.598 \\ b=38.598\sin B \\ (b)/(\sin B)=(34)/(\sin C) \\ (38.598\sin B)/(\sin B)=(34)/(0.811) \\ 38.598\\e41.92 \end{gathered}`

For b and B is not full fill the condition of traiangle so zero triangle from ABC.