Question

In ABC, A = 68°, a = 14 and c = 17. Which of these statements best describes the triangle?

Answer 1

Given for the triangle ABC:

`\begin{gathered} \angle A=68\degree \\ a=14,c=17 \end{gathered}`

Using the sine rule, we will solve the triangle by finding the missing angles

So,

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

substitute with the given data:

`\begin{gathered} (14)/(\sin68)=(17)/(\sin C) \\ \\ \sin C=(17)/(14)\cdot\sin 68=1.125866 \end{gathered}`

The value of (sin C) must be 1 or less than 1

So, the triangle ABC cannot be constructed

The answer will be the last option