Question

Point X is 34m due east of a point Y the bearings of a flagpole from and Y are N18°W and N40°E respectively. Calculate the distance of the flagpole from Y

Answer 1

Explanation:

The diagram representing the scenario is shown in the attached photo. Triangle FXY is formed with F representing the flagpole.

The sum of the angles in a triangle is 180

Angle F = 180 - (50 + 72) = 58°

We want to determine FY, the distance of the flagpole from Y. We would apply the sine rule which is expressed as

a/Sine A = b/SinB = c/SinC

Likening it to the given triangle, it becomes

FY/Sin72 = 34/Sin 58

Cross multiplying, it becomes

FYSin58 = 34Sin72

FY = 34Sin72/Sin58

FY = 34 × 0.951/0.848

FY = 38.13m