Answer:
AB ≈ 24.0 yd
Step-by-step explanation:
Using the Sine Rule in Δ ABC
• [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
a , b , c are the sides opposite ∠ A , ∠ B , ∠ C , respectively.
We require to calculate the measure of ∠ A
The sum of the 3 angles in Δ ABC is 180° , that is
∠ A + ∠ B + ∠ C = 180° ( substitute values )
∠ A + 75° + 63° = 180°
∠ A + 138° = 180° ( subtract 138° from both sides )
∠ A = 42°
Then
a = BC , c = AB , so
[tex]\frac{BC}{sinA}[/tex] = [tex]\frac{AB}{sinC}[/tex] ( substitute values )
[tex]\frac{18}{sin42}[/tex] = [tex]\frac{AB}{sin63}[/tex] ( cross multiply )
AB × sin42° = 18 × sin63° ( divide both sides by sin42° )
AB = [tex]\frac{18sin63}{sin42}[/tex] ≈ 24.0 yd ( to the nearest tenth )