x = 15.1 (1 decimal place)
Step-by-step explanation:
we apply the cosine rule:
a² = b² + c² -2bc CosA
let a = 23, b = 17, c = x
a is the side facing the given angle
CosA = 108°
23² = 17² + x² -2(17)(x)Cos 108
529 = 289 + x²- 34(Cos108)
subtract 289 from both sides:
529 - 289 = x²- 34(Cos108)
240 = x²- 34(Cos108)
240 + 34(Cos108) = x²
240 + 34(-0.3090) = x²
240 - 10.506 = x²
229.494 = x²
Square root both sides:
√229.494 = √x²
x = 15.149
x = 15.1 (1 decimal place)