Answer:
The answer is "38.130".
Step-by-step explanation:
Given:
[tex]Points (Y, X) \\\\F (flagpole)\ make\ a \ triangle[/tex]
Draw Y and X triangles on the underside, and F above them.
Because F is [tex]18^{\circ}[/tex] west from X, so FXY angle measurement [tex]FXY = 72^{\circ}[/tex] from X because F is located [tex]40^{\circ}[/tex] east of north from Y, then
measure of angle [tex]FYX = 50^{\circ}[/tex]
the measure of angle [tex]YFX = 58^{\circ}[/tex] [tex](3 \angle \ of\ triangle = 180^{\circ})[/tex]
Using Law of Sines: [tex]\frac{\sine 58^{\circ}}{34} = \frac{\sine 72^{\circ}}{YF}[/tex]
Cross Multiply:
[tex]YF (\sin 58^{\circ}) = 34(\sin 72^{\circ})\\\\[/tex]
[tex]YF = \frac{34 \sin 72^{\circ}}{\sin 58^{\circ}}\\\\ YF = \frac{34(.951)}{(.848)}\\\\ YF = 38.130[/tex]
