point p and q are respectively 24m north and 7m east of point r.what is the bearing of q and p to the nearest whole number
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To find the bearing of point Q and point P to the nearest whole number, we need to use trigonometry.
First, let's visualize the situation. Let's assume that point R is the reference point (0,0) on a coordinate grid. Point P is located 24m to the north (upwards) and 7m to the east (rightwards) of point R. Point Q is also located north of point R but doesn't have a specific east or west direction mentioned.
To find the bearing, we need to find the angle between the line connecting R to P (RP) and the north direction, as well as the angle between RP and the north direction.
Step 1: Finding the angle between RP and the north direction:
We can use trigonometry to find this angle. We have the lengths of the two sides of a right-angled triangle, with the length of the side opposite the angle (north direction) being 24m and the length of the side adjacent to the angle (east direction) being 7m. Hence, we can use the tangent function:
tanθ = opposite/adjacent
tanθ = 24/7
Using a scientific calculator or an online trigonometry calculator, we can find the angle θ to be approximately 73.74 degrees (to the nearest hundredth).
Step 2: Finding the bearing of P (towards the north):
The bearing is usually given as an angle measured clockwise from the north direction. Since the angle we found (θ) is measured from the east direction counterclockwise, we need to subtract it from 90 degrees to get the bearing in the clockwise direction.
Bearing of P = 90 - θ
Bearing of P = 90 - 73.74
Bearing of P ≈ 16 (to the nearest whole number)
Step 3: Finding the bearing of Q:
Since there is no specific east or west direction mentioned for Q, we need to determine the bearing in relation to point R. In this case, we can use the bearing of P (which we found in Step 2) as a reference.
Because P is located to the east (rightwards) of R, Q will be in the same direction (to the east) or on the opposite direction (to the west) of P. Let's assume Q is to the east of P.
If Q is east of P, the bearing of Q will be the same as the bearing of P. So, the bearing of Q is also approximately 16 (to the nearest whole number).
Therefore, the bearing of point Q and point P, to the nearest whole number, is 16 degrees.