from a point R,300M north of P, a man walks eastwards to a place Q which is 600m from P. find the bearing of P from Q correct to the

nearest degree

tan Ø = 300/600 = 1/2

Ø = 26.565°

so the bearing is 243° or direction of S 27° W

(at times these two terms are interchanged in their meaning, check with your texbook how they define bearing)

240⁰

240° is also an acceptable approximation for the bearing of P from Q.

Well, let's see if we can clown around with some math here!

First, imagine a triangle formed by points P, Q, and R. We want to find the bearing of P from Q, which means we want to find the angle between the line PQ and the north direction.

So, let's break it down. We know that R is 300 meters north of P, and Q is 600 meters from P. Since R is directly north of P, and Q is to the east of R, we have a right-angled triangle.

Using some good ol' Pythagoras, we can find the length of the line QR. The square of the hypotenuse QR is equal to the sum of the squares of the other two sides, PR and PQ.

PR is 300 meters (north) and PQ is 600 meters (east). So, applying Pythagoras, we have:

QR^2 = PR^2 + PQ^2
QR^2 = 300^2 + 600^2
QR^2 = 90000 + 360000
QR^2 = 450000

To find the length, we take the square root of both sides:

QR = √(450000)
QR ≈ 670.83 meters

Now, to find the bearing of P from Q, we need to find the angle. We can use some trigonometry for that!

The bearing angle can be found using the tangent function:

tan(angle) = opposite / adjacent
tan(angle) = 300 / 600
tan(angle) ≈ 0.5

To find the angle, we can take the inverse tangent (or arctan) of 0.5:

angle ≈ arctan(0.5)
angle ≈ 26.57 degrees

So, the bearing of P from Q is approximately 27 degrees (rounded to the nearest degree).

Hope that brought a smile to your face!

To find the bearing of P from Q, we need to visualize the triangle formed by points P, Q, and R.

First, draw a diagram with point P as the origin (0,0). Since point R is 300m north of P, we can mark point R at (0,300) on the graph.

Next, we know that the man walks eastwards to point Q, which is 600m from P. This means that point Q can be marked at (600,0) on the graph.

Now we can calculate the bearing of P from Q. The bearing is the angle measured from the north direction (0 degrees) in a clockwise direction.

To calculate the bearing, we can use the tangent function. The tangent of the angle can be found by dividing the difference in y-coordinates by the difference in x-coordinates.

Tangent(angle) = (Difference in y) / (Difference in x)

In this case, the difference in y is 300 (Q's y-coordinate minus P's y-coordinate) and the difference in x is 600 (Q's x-coordinate minus P's x-coordinate).

Tangent(angle) = 300 / 600 = 1/2

To find the angle, we take the inverse tangent (arctan) of the value we found:

Angle = arctan(1/2) ≈ 26.57 degrees

Therefore, the bearing of P from Q is approximately 26.57 degrees to the nearest degree.