Answer:
|AB| = 240 km (nearest km)
Step-by-step explanation:
Draw a sketch with the given information (attached).
Calculate the missing angle (shown in red on the attached diagram).
Given:
The interior angles of a triangle sum to 180°
⇒ ∠ACB + ∠CAB + ∠CBA = 180°
⇒ ∠ACB + 27° + 66° = 180°
⇒ ∠ACB = 180° - 27° - 66°
⇒ ∠ACB = 87°
Use Sine Rule for sides to calculate |AB|:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{|AB|}{\sin ACB}=\dfrac{|AC|}{\sin CBA}[/tex]
[tex]\implies \sf \dfrac{|AB|}{\sin (87^{\circ})}=\dfrac{220}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=\dfrac{220\:\sin (87^{\circ})}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=240.4899459...[/tex]
[tex]\implies \sf |AB|=240\:km\:(nearest\:km)[/tex]
