Calculate the distance of the flagpole from Y

Question

A point X is 34m due east of a point Y. The bearings of a flagpole from X and Y are north 18 degrees West and north 40 degrees East respectively. Calculate the distance of the flagpole from Y.

Answer 1

Points Y, X, and F (flagpole) make a triangle

 

Draw the triangle with Y and X on the bottom and F located above them

 

Since F is located 18° west of north fromX, then 

      measure of angle FXY = 72°

 

Since F is located 40° east of north from Y, then

      measure of angle FYX = 50°

 

measure of angle YFX = 58° (3 angles of triangle = 180°)

 

Using Law of Sines:  Sine 58°/34 = Sine 72°/YF (distance sought)

 

Cross Multiply:  YF (Sin 58°) = 34(Sin 72°)

 

                                     YF = 34(Sin 72°)/(Sin 58°)

 

                                     YF = 34(.951)/(.848)

 

                                     YF = 38.130