Answer:
m∠B = 70.0° (nearest tenth)
Step-by-step explanation:
Sine Rule for Angles
[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)
Given:
Substituting the given values into the formula to find m∠C:
[tex]\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}[/tex]
[tex]\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}[/tex]
[tex]\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)[/tex]
[tex]\implies \sf m \angle C=69.96086904^{\circ}[/tex]
Interior angles of a triangle sum to 180°
[tex]\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}[/tex]
[tex]\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}[/tex]
[tex]\implies \sf m \angle B=70.03913...^{\circ}[/tex]
Therefore, m∠B = 70.0° (nearest tenth)
