Question

Please help find them
1 AB

2 BC​

Answer 1

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 )