Answer:
The distance of flag post from Y is 38.13 m
Step-by-step explanation:
Consider point Y at the intersection of both lines as shown below. Now the point X lies 34 meter from point Y in east direction.
Now flag pole at point X lies at a bearing of N18°W. That is at point X from north, flag post makes an angle of 18° towards west.
Similarly flag pole at point Y lies at a bearing of N40°E. That is at point Y from north, flag post makes an angle of 40° towards east.
Consider ∆ AXY as right angle triangle. Therefore measure of angle FXY is,
[tex]\angle AXY=\angle AXF+\angle FXY[/tex]
[tex] \therefore 90 \degree=18\degree+\angle FXY [/tex]
[tex] \angle FXY=72\degree [/tex]
Consider ∆ BYX as right angle triangle. Therefore measure of angle FYX is,
[tex]\angle BYX=\angle BYF+\angle FYX[/tex]
[tex] \therefore 90 \degree=40\degree+\angle FYX [/tex]
[tex] \angle FYX=50\degree [/tex]
Refer attachment 1.
From diagram consider the triangle FYX. To find the third angle that is ∠YFX can be calculated by using angle sum property of triangle.
∠YFX+∠FYX+∠FXY=180°
∠YFX+50°+72°=180°
∠YFX=58°
Refer attachment 2.
Now the distance FY can be calculated using sin rule as follows,
[tex]\frac{\sin X}{FY}=\frac{\sin F}{YX}=\frac{\sin Y}{FX}[/tex]
Substituting the values,
[tex]\frac{\sin 72}{FY}=\frac{\sin 58}{34}=\frac{\sin 50}{FX}[/tex]
Simplifying first two terms,
[tex]\frac{\sin 72}{FY}=\frac{\sin 58}{34}[/tex]
Cross multiplying,
[tex]34\times\sin 72=FY\times \sin 58[/tex]
[tex]\dfrac{34\times\sin 72}{\sin 58}=FY[/tex]
[tex]FY=38.13[/tex] m
