Answer:
1) ∠AEB ≈ 83.7°
2) CE = 6.1 cm
3) BC ≈ 7.1 cm
Explanation:
1) Use theorem of cosine
c² = a² + b² - 2ab*cos(α)
4.5² = 3² + 3.7² - 2*3*3.7 *cos(∠AEB)
cos(∠AEB) = (4.5² - 3² - 3.7²) /(- 2*3*3.7) = 0.11
∠AEB = arc cos(∠AEB) = arc cos(0.11) ≈ 83.7°
2)
∠CED =∠AEB = 83.7° as vertical angles
Use law of sine
CD/sin(∠CED) = CE/ sin(∠CDE)
7/sin(83.7) = CE/sin(60°)
CE = 7*sin(60°)/sin(83.7°) = 6.1 cm
3.
∠BEC + ∠CED = 180°
∠BEC = 180° - ∠CED = 180° - 83.7° = 96.3°
Use theorem of cosine
c² = a² + b² - 2ab*cos(α)
BC² = BE² + CE² - 2 BE * EC *cos(∠BEC)
BC² = 3² + 6.1² - 2*3 * 6.1 *cos(96.3°) ≈ 50.23 cm
BC = √(50.23)≈ 7.1 cm