Question

Please help find them 1 AB2 BC​

Answer 1

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 = $\sqrt{246.63}$ ≈ 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

$\frac{BC}{sin53}$ = $\frac{BD}{sin32}$ = $\frac{12.4}{sin32}$ ( cross- multiply )

BC × sin32° = 12.4 × sin53° ( divide both sides by sin32° )

BC = $\frac{12.4sin53}{sin32}$ ≈ 18.7 cm ( to 1 dec. place )