Answer:
AB ≈ 24.0 yd
Step-by-step explanation:
Using the Sine Rule in Δ ABC
• \(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)
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
\(\frac{BC}{sinA}\) = \(\frac{AB}{sinC}\) ( substitute values )
\(\frac{18}{sin42}\) = \(\frac{AB}{sin63}\) ( cross multiply )
AB × sin42° = 18 × sin63° ( divide both sides by sin42° )
AB = \(\frac{18sin63}{sin42}\) ≈ 24.0 yd ( to the nearest tenth )
