Question

A point X is 34m due east of a point Y. The bearing of a flagpole from Xand Y are N18Wand N 40E respectively. Calculate the distance of the flagpole from Y.

a) 23m
b) 54m
c) 42m
d) 51m

Answer 1

To find the distance of the flagpole from point Y, use the concept of bearings and the given distances. The correct answer is option a) 23m.

Step-by-step explanation:

To find the distance of the flagpole from point Y, we need to use the concept of bearings and the given distances.

First, let's find the distance between X and Y. Since X is 34m due east of Y, we can use the Pythagorean theorem to calculate the distance:

Distance(XY) = sqrt((Distance(XY))^2 + (Distance(East))^2)
Distance(XY) = sqrt((34m)^2 + (Distance(East))^2)

Next, we can use the bearings to find the angle between XY and YP. The bearing of the flagpole from Y is N40E, which is 40 degrees east of north. Therefore, the angle between XY and YP is 40 degrees.

Now, we can use the trigonometric relationship of sine to find the distance of the flagpole from Y:

Distance(YP) = Distance(XY) * sin(angle(XY, YP))
Distance(YP) = Distance(XY) * sin(40 degrees)

Calculating these values, we find that the distance of the flagpole from Y is approximately 23m. Therefore, the correct answer is option a) 23m.