two boats a and left a port c at the same time on different route b travelled on a bearing of 150 and a travelled on the north side of b when a had travelled 8km and b travelled 10km the distance between the two boats was found to be 12km calculate the bearing of route a from c
Let me repost your question in proper English:
Two boats A and B left a port C at the same time on different routes. B travelled on a bearing of 150° and A travelled on the north side of B. When A had travelled 8 km and B travelled 10 km, the distance between the two boats was found to be 12 km. Calculate the bearing of the route A from C.
Start by sketching line CB for which you are given the distance and direction.
Complete triangle ABC. You now have a triangle with all 3 sides given.
We can find angle C using the Cosine Law.
12^2 = 8^2 + 10^2 - 2(8)(10)cos C
160cos C = 64 + 100 - 144
cos C = 1/8
Find angle C, and then you can state the bearing using the original direction of 150°
Traveled on a HEADING !
If I look at the lighthouse through a hand bearing compass, that is a "bearing".
If I steer a compass course, that is a "heading".
The second use of "bearing" is correct:
"Calculate the bearing of the route A from C."
( math talk drives me crazy)
Actually bearing of BOAT A from C ( which is the heading of A if there is no wind or current.)
The question is a little bit complicated
Have tried my best but cant get it
Someone should kindly please give me some hints 🙃🙃😔😔😪😪
Two boats A and B left a port C at the same time on different routes. B travelled on a bearing of 150° and A travelled on the north side of B. When A had travelled 8 km and B travelled 10 km, the distance between the two boats was found to be 12 km. Calculate the bearing of the route A from C.? Hints needed pls?
To calculate the bearing of route A from point C, we can use trigonometry and the information provided.
First, let's draw a diagram to better understand the situation:
C
/
/|
/ |
12 / | 8 km
/ |
/ |
/ θ |
/_____|
A 10 km B
In this diagram, A represents boat A, B represents boat B, and C represents the starting point (port).
From the information given, we know that when A has traveled 8 km and B has traveled 10 km, the distance between the two boats is 12 km. This forms a right-angled triangle.
Let's label the angle between route A and the line joining A and C as θ.
Using the trigonometric relationship in a right triangle:
sin(θ) = opposite/hypotenuse
We can substitute the values we have:
sin(θ) = 8 km / 12 km
sin(θ) = 2/3
To find the angle θ, we take the inverse sine (also called arcsine) of both sides:
θ = arcsin(2/3)
Using a calculator, we find that arcsin(2/3) ≈ 41.81 degrees.
Therefore, the bearing of route A from point C is approximately 41.81 degrees.