Question

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 1

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.

Answer 2

H=(a)(sinC)=19(sin37)

Therefore h ≈11.43

Since c<h, no triangle is formed.