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 )
