∠B = 77°, a = 7.42 and b = 12.61
Solution:
Given triangle ABC.
∠A = 35°, ∠C = 68°, c = 12
To find the measure of ∠B:
Sum of all the angles of the triangle = 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ 35° + ∠B + 68° = 180°
⇒ 103° + ∠B = 180°
⇒ ∠B = 180° – 103°
⇒ ∠B = 77°
To find the length of a and b:
The side opposite to angle A is a.
The side opposite to angle B is b.
Using law of sine,
[tex]$\frac{\sin C}{c}=\frac{\sin A}{a}[/tex]
[tex]$\frac{\sin 68^\circ}{12}=\frac{\sin 35^\circ}{a}[/tex]
[tex]$\frac{0.9271}{12}=\frac{0.57357}{a}[/tex]
Do cross multiplication, we get
[tex]$0.9271a=6.88284[/tex]
Divide by 0.9271 on both sides, we get
⇒ a = 7.42
Again by law of sine,
[tex]$\frac{\sin C}{c}=\frac{\sin B}{b}[/tex]
[tex]$\frac{\sin 68^\circ}{12}=\frac{\sin 77^\circ}{b}[/tex]
[tex]$\frac{0.9271}{12}=\frac{0.9744}{b}[/tex]
Do cross multiplication, we get
[tex]$0.9271b=11.6928[/tex]
Divide by 0.9271 on both sides, we get
⇒ b = 12.61
Hence ∠B = 77°, a = 7.42 and b = 12.61.
