Answer:
AB ≈ 15.7 cm, BC ≈ 18.7 cm
Step-by-step explanation:
(1)
Using the Cosine rule in Δ ABD
AB² = 12.4² + 16.5² - (2 × 12.4 × 16.5 × cos64° )
= 153.76 + 272.25 - (409.2 cos64° )
= 426.01 - 179.38
= 246.63 ( take the square root of both sides )
AB = [tex]\sqrt{246.63}[/tex] ≈ 15.7 cm ( to 1 dec. place )
(2)
Calculate ∠ BCD in Δ BCD
∠ BCD = 180° - (53 + 95)° ← angle sum in triangle
∠ BCD = 180° - 148° = 32°
Using the Sine rule in Δ BCD
[tex]\frac{BC}{sin53}[/tex] = [tex]\frac{BD}{sin32}[/tex] = [tex]\frac{12.4}{sin32}[/tex] ( cross- multiply )
BC × sin32° = 12.4 × sin53° ( divide both sides by sin32° )
BC = [tex]\frac{12.4sin53}{sin32}[/tex] ≈ 18.7 cm ( to 1 dec. place )
