Answer :

Answer:

b ≈ 14.1

Step-by-step explanation:

Using the Law of Sines in the triangle

• [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

a, b and c are the sides opposite ∠ A, ∠ B and ∠ C

Using the first 2 ratios of the law of sines , that is

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]

let a = 10, ∠ A = 30° and ∠ B = 180° - (105 + 30)° = 180° - 135°  = 45°

substitute these values into the 2 ratios

[tex]\frac{10}{sin30}[/tex] = [tex]\frac{b}{sin45}[/tex] ( cross multiply )

b × sin30° = 10 × sin45° ( divide both sides by sin30° )

b = [tex]\frac{10sin45}{sin30}[/tex] ≈ 14.1 ( to the nearest tenth )