Answer:
This is a ssa situation, no triangle is possible.
Step-by-step explanation:
"SSA" means "Side, Side, Angle".
In an SSA triangle, we are given two sides and an angle that is not the angle between the given sides.
In triangle ABC:
- A, B and C are the interior angles.
- a, b and c are the sides opposite the corresponding interior angles.
Given:
- m∠A = 44°
- side a = 12.6 cm
- side b = 19 cm
The angle that is between the sides a and b is angle C.
Therefore, as angle A is not the angle between the given sides, ΔABC is an SSA triangle.
Law of Sines
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
To determine if any triangles are possible, substitute the given values into the Law of Sines to find angle B:
[tex]\implies \sf \dfrac{\sin 44^{\circ}}{12.6}=\dfrac{\sin B}{19}[/tex]
[tex]\implies \sf \sin B=\dfrac{19\sin 44^{\circ}}{12.6}[/tex]
[tex]\implies \sf \sin B=1.0475007...[/tex]
As -1 ≤ sin B ≤ 1, there is no solution for angle B.
Therefore, although this is an SSA situation, no triangle is possible.
