Question

Can someone help explain this to me? I don’t think I’m doing it right.

Answer 1

∠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,

$\frac{\sin C}{c}=\frac{\sin A}{a}$

$\frac{\sin 68^\circ}{12}=\frac{\sin 35^\circ}{a}$

$\frac{0.9271}{12}=\frac{0.57357}{a}$

Do cross multiplication, we get

$0.9271a=6.88284$

Divide by 0.9271 on both sides, we get

⇒ a = 7.42

Again by law of sine,

$\frac{\sin C}{c}=\frac{\sin B}{b}$

$\frac{\sin 68^\circ}{12}=\frac{\sin 77^\circ}{b}$

$\frac{0.9271}{12}=\frac{0.9744}{b}$

Do cross multiplication, we get

$0.9271b=11.6928$

Divide by 0.9271 on both sides, we get

⇒ b = 12.61

Hence ∠B = 77°, a = 7.42 and b = 12.61.