The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. C = 37°, a = 19, c = 8
Answer:
According to the sin law,
For a triangle ABC,
In which AB, BC and CA are the edges of the triangle,
And, ∠ A , ∠ B and ∠ C are the angles of the triangle.
Here, AB = 8 unit BC = 19 unit and ∠ C = 37°
According to the sin law,
For triangle ABC,
\(\frac{BC}{AB} = \frac{sin A}{sin C}\)
⇒ \(\frac{19}{8} = \frac{sin A}{sin 37^{\circ}}\)
⇒ \(2.375\times sin 37^{\circ} = sin A\)
⇒ \(sin A=1.42931067999\)
Which is not possible.
Because -1 ≤ sin A ≤ 1
Thus, the triangle ABC can not be possible.