two boats a and b left a port at the same time on different routes. b travelled on a bearing of 150 and a travelled on north side of b. when a had travelled 8km and b had travelled 10km, the distance between the two boats was found to be 12km calculate the bearing of a route from c
i have not seen the solution to my question
Patience, child!! We are human beings who volunteer to help students. We are not here 24/7. A math tutor will try to help you when s/he is online.
geez - impatient much?
Draw it, and if you call the starting point O, then you have a triangle OAB with a=10, b=8. So, you can find angle O = θ using the law of cosines:
8^2 + 10^2 - 2*8*10*cosθ = 12^2
cosθ = 1/8
θ = 82.8°
So you know that the bearing of A from O is 150-82.8 = 67.2°
Now just do the usual calculations to find the actual locations of A and B, relative to O.
Maybe by then you will know what the heck "c" is.
To calculate the bearing of boat A's route from point C, we need to find the angle between the north direction (from point B) and the line connecting point B to point C. Here's how we can determine the bearing:
1. Draw a diagram to visualize the situation. Label point A as the starting point of boat A, point B as the starting point of boat B, and point C as the intersection point of both routes.
2. Since boat B traveled on a bearing of 150, we know that the line from B to C makes a clockwise angle of 150 degrees with the north direction. So, draw a line from B at an angle of 150 degrees clockwise from the north direction.
3. We are given that boat A traveled on the north side of boat B. Therefore, from the 12km distance between the two boats and the information that A traveled 8km while B traveled 10km, we can deduce that the line connecting A to C forms a right triangle with the line connecting B to C.
4. Use the Pythagorean theorem to find the length of the line AC. Let's call it x:
x^2 = BC^2 - AB^2
x^2 = 12^2 - 8^2
x^2 = 144 - 64
x^2 = 80
x = sqrt(80)
x = 8sqrt(5)
5. Now, we have all the sides of the right triangle formed by lines AB, BC, and AC. We can use trigonometric functions to find the angles of the triangle.
6. Since we have the length of AB (8km) and BC (10km), we can calculate the angle formed by line BC:
cos(angle BC) = AB / BC
cos(angle BC) = 8 / 10
angle BC = arccos(8/10)
7. Using a calculator, find the angle BC: arccos(8/10) ≈ 38.66 degrees.
8. Now, we can calculate the bearing of A's route from C by subtracting the angle BC from 360 degrees (since bearings are measured clockwise from the north direction):
Bearing of A's route from C = 360 - angle BC
Bearing of A's route from C ≈ 360 - 38.66
Bearing of A's route from C ≈ 321.34 degrees
Therefore, the bearing of boat A's route from point C is approximately 321.34 degrees.