A town Q is in a bearing of 210° from P,R is another town on a bearing of 150° from P east of Q.The distance between R and P is10km .find the distance between R and Q
Given: PQ = 210o, PR = 10km[150o], QR = ?.
210-150 = 60o = Angle between given vectors.
Law of sine: RQ/sin60 = 10/sin60
QR = 10*sin60/sin60 = 10 km.
Interesting and satisfactory
P=60°,Q=60°,R=60°
PR=10km
PR= ?
Using sine rules p/sinP= q/sinQ= r/sinR
P/sin60°= 10/sin60° cross multiply
After the working
QR is equal to 10km.
If origin of x y axis system at P
Q is 210 -180 = 30 degrees above -y axis
R is 90 + 60 degrees or 60 below +x direction from Q
that means angle PQR is ALSO 30 deg !
so QR = RP = 10
can i see the correct answer
A town q is on a bearing of 210degree from p, R is another town on a bearing of 150degree from p east of q, the distance between R and p is 10km, find the distance between R and q
To find the distance between R and Q in this scenario, we can use trigonometry and the given information.
First, let's draw a diagram to visualize the situation. Let P be the starting point, Q be the town on a bearing of 210°, and R be the town on a bearing of 150° east of Q. We are given that the distance between R and P is 10 km.
```
Q
/
/
/
P ---- R
```
Next, let's break down the problem into smaller parts. We need to find the distance between Q and R, which involves finding the distance from Q to P and subtracting the distance from P to R.
We're given that the distance from P to R is 10 km. However, before we can find the distance from Q to R, we need to find the distance from Q to P.
To find the distance from Q to P, we can use the concept of bearing. A bearing is an angle measured clockwise from the north direction. Therefore, if Q is at a bearing of 210° from P, we can say that the bearing from P to Q is 180° + 210° = 390°.
Now, let's use trigonometry to find the distance from Q to P. We'll use the formula:
cos(angle) = adjacent/hypotenuse
In this case, the angle is 390° and the hypotenuse is the distance from Q to P (let's call it x). The adjacent side is the distance between Q and R, which we want to find.
cos(390°) = adjacent/x
Next, we solve for x: the distance from Q to P.
x = adjacent / cos(390°)
Now that we have the distance from Q to P, we can find the distance from R to Q by subtracting the distance from P to R (10 km) from the distance from Q to P.
Distance from R to Q = Distance from Q to P - Distance from P to R
Substituting the values we've found:
Distance from R to Q = x - 10 km
Finally, we have the distance from R to Q. Plug in the value of x to get the final answer.