A point x is 34m due to east of a point Y . The bearing of a flagpole from x and Y are N18°W And N40°E respectively .
Calculate the distance of the flagpole from Y .
Using sine rule And if possible a sketched drawing

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,  

Consider ∆ BYX as right angle triangle. Therefore measure of angle FYX is,  

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,  

Substituting the values,

Simplifying first two terms,

Cross multiplying,

m

b

a

step-by-step explanation: