Question

A point X is 34m due east of a point Y.The bearing of a flagpole from X and Y are N18W and N40E respectively calculate the distance of the flag pole from Y

Answer 1

Answer:

The answer is "38.130".

Step-by-step explanation:

Given:

$Points (Y, X) \\\\F (flagpole)\ make\ a \ triangle$

Draw Y and X triangles on the underside, and F above them.

Because F is  $18^{\circ}$  west from X, so FXY angle measurement $FXY = 72^{\circ}$ from X  because F is located $40^{\circ}$  east of north from Y, then

     measure of angle $FYX = 50^{\circ}$

 the measure of angle $YFX = 58^{\circ}$ $(3 \angle \ of\ triangle = 180^{\circ})$

Using Law of Sines: $\frac{\sine 58^{\circ}}{34} = \frac{\sine 72^{\circ}}{YF}$  

 Cross Multiply:  

$YF (\sin 58^{\circ}) = 34(\sin 72^{\circ})$

$YF = \frac{34 \sin 72^{\circ}}{\sin 58^{\circ}}\\\\ YF = \frac{34(.951)}{(.848)}\\\\ YF = 38.130$