Answer:
[tex]\boxed{\boxed{b=13.8}}[/tex]
Step-by-step explanation:
In triangle ABC it is given that,
[tex]m\angle A=35^{\circ},m\angle B=65^{\circ},c=15[/tex]
We know that in a triangle sum of all three angle is 180°, so
[tex]\Rightarrow m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]
[tex]\Rightarrow m\angle C=180^{\circ}-m\angle A-m\angle B[/tex]
[tex]\Rightarrow m\angle C=180^{\circ}-35^{\circ}-65^{\circ}[/tex]
[tex]\Rightarrow m\angle C=80^{\circ}[/tex]
Applying the Sine law,
[tex]\Rightarrow \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
[tex]\Rightarrow \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
[tex]\Rightarrow \dfrac{\sin 65^{\circ}}{b}=\dfrac{\sin 80^{\circ}}{15}[/tex]
[tex]\Rightarrow \dfrac{b}{15}=\dfrac{\sin 65^{\circ}}{\sin 80^{\circ}}[/tex]
[tex]\Rightarrow b=\dfrac{\sin 65^{\circ}\times 15}{\sin 80^{\circ}}[/tex]
[tex]\Rightarrow b=13.8[/tex]
