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Please help find them
1 AB

2 BC​

Please help find them 1 AB 2 BC​-example-1
User Tules
by
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1 Answer

3 votes

Answer:

AB ≈ 15.7 cm, BC ≈ 18.7 cm

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 =
√(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


(BC)/(sin53) =
(BD)/(sin32) =
(12.4)/(sin32) ( cross- multiply )

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

BC =
(12.4sin53)/(sin32) ≈ 18.7 cm ( to 1 dec. place )

User Iacks
by
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