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pickupchik [31]
2 years ago
10

Please help find them 1 AB2 BC​

Mathematics
1 answer:
spin [16.1K]2 years ago
6 0

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 )

         

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