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

h=(a)(sinC)=19(sin37)

Therefore h ≈11.43

Since c<h, no triangle is formed.

Answer 2

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,

`(BC)/(AB) = (sin A)/(sin C)`

⇒
`(19)/(8) = (sin A)/(sin 37^(\circ))`

⇒
`2.375* 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.