The bearing of Q from P is 150
0 and the bearing of P from R is 015
0
. If Q and R are 24km
and 32km respectively from P:
(i) represent this information in a diagram;
(ii) Calculate the distance between Q and R, correct to two decimal places;
(iii) Find the bearing of R from Q, correct to the nearest degree.
Cannot diagram on these posts.
once you have drawn your triangle PQR, note that angle P is 105°
so use the law of cosines to find QR
then use the law of sines to find angle Q. That will let you figure the bearing of Q from P.
Post your work if you get stuck.
(i) To represent this information in a diagram, we can start by drawing three points: P, Q, and R.
- Place P in the center of the diagram.
- Draw a line segment from P to Q, representing the 24km distance between them.
- Draw another line segment from P to R, representing the 32km distance between them.
- Label the angle formed at P as 150 degrees, which represents the bearing of Q from P.
- Label the angle formed at P as 15 degrees, which represents the bearing of P from R.
The diagram should now illustrate the positions of P, Q, and R, along with the respective distances and bearings.
(ii) To calculate the distance between Q and R, we can use the Pythagorean theorem since we have a right triangle formed by P, Q, and R.
- Let's denote the distance between Q and R as x.
- We now have a right triangle with the following sides:
- The side opposite angle 150 degrees is the distance between Q and P, which is 24km.
- The side opposite angle 15 degrees is the distance between P and R, which is 32km.
- The hypotenuse, which represents the distance between Q and R, is denoted as x.
Applying the Pythagorean theorem, we have:
x^2 = 24^2 + 32^2
x^2 = 576 + 1024
x^2 = 1600
x = √1600
x = 40 km
So, the distance between Q and R is 40 km.
(iii) To find the bearing of R from Q, we can use simple subtraction.
- The bearing of Q from P is given as 150 degrees.
- To find the bearing of R from Q, subtract the bearing of P from R (015 degrees) from the bearing of Q from P (150 degrees):
Bearing of R from Q = 150 degrees - 15 degrees = 135 degrees.
Therefore, the bearing of R from Q is 135 degrees.