point P and Q are respectively 24m north and 7m east of point R. What is bearing of Q and P to the nearest whole degree.(a)52(b)164(c)134(d)159
Ans
To find the bearing of point Q and P, we can use trigonometry.
Step 1: Draw a diagram and label the points:
```
N
|
|
|______ E
R
```
Step 2: Mark the direction of North (N) and East (E) on the diagram.
Step 3: Draw lines to represent the distances from point R to point P and Q.
```
N
|
| P
| |
|_________|______ E
R Q
```
Step 4: Determine the angle between the line connecting R and P, and the line connecting R and Q.
We can use the tangent function to find this angle.
```
tangent(angle) = opposite / adjacent
```
The angle between the R and P line and the horizontal axis (East) can be found by taking the inverse tangent of the opposite side (24m) divided by the adjacent side (7m).
```
angle_P = arctan(24/7)
```
Similarly, the angle between the R and Q line and the horizontal axis (East) can be found by taking the inverse tangent of the opposite side (7m) divided by the adjacent side (24m).
```
angle_Q = arctan(7/24)
```
Step 5: Convert the angles to bearing.
Bearing is measured from North (N) in a clockwise direction. We need to find the bearing of P and Q to the nearest whole degree.
To do this, we need to add 90 degrees to the angle measured above in order to align with the North direction.
```
bearing_P = angle_P + 90
bearing_Q = angle_Q + 90
```
Step 6: Round the bearings to the nearest whole degree.
```
bearing_P ≈ 150 degrees
bearing_Q ≈ 112 degrees
```
Comparing the rounded bearings to the options given, the answer would be (c) 134 degrees.
To determine the bearing of point P and Q to the nearest whole degree, we need to use trigonometry.
First, let's draw a diagram to visualize the situation. We have a triangle with point R at the vertex and points P and Q located 24m north and 7m east of R, respectively.
R
/|\
/ | \
/ | \
24m / | \ 7m
/ | \
P-----R-----Q
Next, we can use the tangent function to find the angle of Q. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 7m (east) and the adjacent side is 24m (north). Therefore, the tangent of the angle of Q can be calculated as:
tan(Q) = opposite / adjacent = 7m / 24m
Using a calculator or a trigonometric table, we can find the value of Q. Taking the inverse tangent (arctan) of the result will give us the angle in degrees.
arctan(7/24) ≈ 16.26 degrees
The bearing of point Q is measured clockwise from the north, so the answer is approximately 16 degrees.
Similarly, we can use the same approach to find the bearing of point P. The tangent function provides the angle formed between the north direction and the line connecting R and P.
tan(P) = opposite / adjacent = 24m / 7m
arctan(24/7) ≈ 73.34 degrees
The bearing of point P is then approximately 73 degrees.
To determine the nearest whole degree, we round these values:
Q ≈ 16 degrees
P ≈ 73 degrees
Therefore, the correct option is (b) 164 degrees, which is the nearest whole degree to the bearing of point Q.
(b)
is the bearing of Q from P
180 - arctan(7/24)