Musah stands at the center of a rectangular field.He takes 50 steps north,then 25 steps West and finally 50 on a bearing of 315°. Sketch Musah's movement How far west is Musah's final point from the center? How far north is Musah's final point from the center?

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-08-10T08:36:42+02:00

Answer:

The distance of Musah's final point from the center in the west direction is 60.355 steps

The distance of Musah's final point from the center in the north direction is 85.355 steps

Step-by-step explanation:

Given that :

Musah stands at the center of a rectangular field.

He takes 50 steps north, then 25 steps West and finally 50 on a bearing of 315°.

The sketch for Musah's movement is seen in the attached file below.

How far west is Musah's final point from the centre?

In order to determine how far west is Musah's,

Let d be the distance of how far west;

Then d = BC + CD cos θ

In the North West direction,

cos θ = cos 45°

d = 25 + 50( cos 45°)

d = 25 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex] )

d = 25 + 50( 0.7071)

d =25 + 35.355

d = 60.355 steps

How far north is Musah's final point from the center?

Let d₁ be the distance of how far North;

Then d₁ = AB + CD sin θ

d₁ = 50 + 50 sin 45°

d₁ = 50 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex] )

d₁ = 50 + 50( 0.7071)

d₁ = 50 + 35.355

d₁ = 85.355 steps