P is 49km away from q on a bearing of 135°.z is 64km away from R on a bearing of 225°find the distance of z from q and bearing of z from q
I need an answer I don't no how to solve it
since you have not given any relation between PQ and ZR there is no way to figure this out.
If you mean Z is 64km from P:
ZQ = QP + PZ.
ZQ = 49[135o] + 64[225o],
X = 49*sin135 + 64*sin225 = -10.61 km.
Y = 49*Cos135 + 64*Cos225 = -79.90 km.
ZQ = -10.61 - 79.9i = 80.6km[7.56o] W. of S. = 80.6km[187.6o] CW.
To find the distance of point Z from point Q and the bearing of Z from Q, we need to use trigonometry and the concept of bearings.
First, let's draw a diagram to visualize the situation.
```
P
\
\
\
Q --- Z
/
/
/
R
```
Given information:
- P is 49 km away from Q on a bearing of 135°.
- Z is 64 km away from R on a bearing of 225°.
To find the distance of Z from Q, we can use the Pythagorean theorem. Since P is directly opposite to Z and forms a right angle with Q, we can consider PZQ as a right triangle.
Using the Pythagorean theorem:
(QZ)^2 = (PQ)^2 + (PZ)^2
Substituting the given values:
(QZ)^2 = (49)^2 + (64)^2
Calculating:
(QZ)^2 = 2401 + 4096
(QZ)^2 = 6497
Taking the square root of both sides:
QZ ≈ √6497
QZ ≈ 80.59 km
Therefore, the distance of Z from Q is approximately 80.59 km.
Now, let's determine the bearing of Z from Q. To do this, we need to understand the concept of bearings.
Bearings are angles measured clockwise from the north direction. In this context, the reference direction is the positive x-axis. So, we need to find the bearing of Z, starting from the positive x-axis and moving clockwise.
To find the bearing, we can use trigonometry. Since we have a right triangle PZQ, we can consider the ratio of the lengths of the sides.
tan(angle) = opposite / adjacent
tan(bearing) = PQ / ZQ
Substituting the given values:
tan(bearing) = 49 / 80.59
Calculating:
bearing ≈ tan^(-1)(49/80.59)
Using a calculator, we get:
bearing ≈ 29.82°
Therefore, the bearing of Z from Q is approximately 29.82°.