Answer:
The answer is (a) ⇒ x = 3.5
Step-by-step explanation:
In ΔABZ use the sin rule to find ∠ABZ and ∠BAZ
∵ AB/sin50° = AZ/sin∠ABZ
∴ 8.8/sin50° = 4.79/sin∠ABZ
∴ sin∠ABZ = (4.79 × sin50) ÷ 8.8
∴ sin ABZ = 0.416971
∴m∠ABZ = 24.64°
∴ m∠BAZ = 180 - (50 + 24.64) = 105.36°
In ΔABZ use the cosine rule to find BZ
(BZ)² = (BA)² + (AZ)² - 2(BA)(AZ)cos∠BAZ
∵ (BZ)² = (8.8)² + (4.79)² - 2(8.8)(4.79)cos105.36°
∴ (BZ)² = 122.7147953
∴ BZ = 11.078
Use the cosine rule in ΔCBZ to find CZ
(CZ)²= (BC)² + (BZ)² - 2(BC)(BZ)cos∠B
∵ (CZ)² = (4.79)² + (11.078)² - 2(4.79)(11.078)cos39²
∴ (CZ)² = 63.18982803
∴ CZ = 7.949
∵ CZ = 2x + 1
∴ 2x + 1 = 7.949
∴ 2x = 7.949 - 1 = 6.949
∴ x = 6.949 ÷ 2 = 3.47 ≅ 3.5
