Given:
∠A = 66°
AB = 5 mi
To find:
The distance from point B to point C.
Solution:
Using trigonometric ratio formula:
[tex]$\tan \theta=\frac{\text { Opposite side of } \theta}{\text { Adjacent side of } \theta}[/tex]
[tex]$\tan A =\frac{\text { Opposite side of } A }{\text { Adjacent side of } A}[/tex]
[tex]$\tan 66^\circ =\frac{BC}{AB}[/tex]
[tex]$2.25 =\frac{BC}{5}[/tex]
Multiply by 5 on both sides.
[tex]$5\times 2.25 =5\times \frac{BC}{5}[/tex]
[tex]$11.2 = BC[/tex] (nearest tenth)
The distance from point B to point C is 11.2 mi.
