h=(a)(sinC)=19(sin37)
That means h β11.43
Since c<h, There is no triangle
The Dimensions of triangle are
Β B=111Β°, c=8 , b=12
Β First we will use Cosine Law to Determine , measurement of third side.
Β Β [tex]\cos B=\frac{b^2+c^2-a^2}{2bc}\\\\ \cos 111^{\circ}=\frac{(12)^2+(8)^2-a^2}{2 \times 12 \times 8}\\\\-0.35836=\frac{144+64-a^2}{192}\\\\-68.80=208-a^2\\\\a^2=208+68.80\\\\a^2=276.80\\\\a=\sqrt{276.80}\\\\a=16.64[/tex]
To Form a Triangle ,Sum of two sides of a triangle should be greater than third side.
a=16.64 , b=12, c=8
Angle in front of Side 12 unit has measure 111Β°, which is an Obtuse Angle.Also Length of Other side is 16.64 unit, so This Angle should also be greater than 111Β°, But sum of three angles of Triangle is equal to 180Β°.So, This triangle is not Possible.
