starting from A truck travels 10 km north to B then 13km west to C find the bearing of C from
Well, let me get my compass, clown nose, and funny bone ready for this! So, let me understand, the truck went 10 km north from point A to point B and then 13 km west from point B to point C. Alright, I'm ready to calculate the bearing of point C.
To find the bearing of C from A, we need to remember that bearings are always measured clockwise from the north. So, let's draw a triangle ABC and figure out the angles and distances.
Now, let's pretend the truck driver is a pirate searching for buried treasures. The truck traveled 10 km north, which means it travelled directly up the treasure map. Then it turned 13 km west, which means it went left on the map.
So, we have a right-angled triangle with the hypotenuse as the truck's path from A to C. To find the bearing, we need to find the angle that the hypotenuse makes with the north direction.
Using the good old Pythagorean theorem, we can find the length of the hypotenuse. From A to C, it's like the truck took the scenic route!
The distance between A and C is (10^2 + 13^2)^0.5. Yes, I did math! That's approximately 16.401 km.
Now, to find the bearing, we need to find the angle. We can use some trigonometry, specifically the inverse tangent (arctan) function.
The angle is given by arctan(13/10). And after consulting a very serious clown mathematician, I can assure you the angle is approximately 51.34 degrees.
So, the bearing of point C from point A is 51.34 degrees from the north. Just make sure your compass can handle all this pirate-level craziness!
To find the bearing of point C from point A, we can use trigonometry.
Given that the truck travels 10 km north from A to B and then 13 km west from B to C, we can sketch a triangle to represent the distances. Let's use point A as the starting point, point B as the northward destination, and point C as the westward destination.
Now, let's find the distance between points A and C. We can use the Pythagorean theorem:
AC² = AB² + BC²
AC² = (10 km)² + (13 km)²
AC² = 100 km² + 169 km²
AC² = 269 km²
Taking the square root of both sides, we find:
AC = √(269)
AC ≈ 16.4 km
Next, let's find the angle that AC makes with the north direction. We can use the inverse tangent function:
tan(theta) = opposite/adjacent
tan(theta) = BC/AB
tan(theta) = 13 km/10 km
tan(theta) ≈ 1.3
Taking the arctan of both sides, we find:
theta ≈ arctan(1.3)
theta ≈ 53°
Therefore, the bearing of point C from point A is approximately 53°.
To find the bearing of point C from A, we can use trigonometry. The bearing represents the angle between the north direction and the line connecting A to C.
To begin, visualize a right-angled triangle with A as the right angle, B to the north of A, and C to the west of B. The side AB represents the distance traveled north, which is 10 km, and side BC represents the distance traveled west, which is 13 km.
First, we need to find the length of the hypotenuse AC. By using the Pythagorean theorem, we can calculate it:
AC² = AB² + BC²
AC² = 10² + 13²
AC² = 100 + 169
AC² = 269
Taking the square root of both sides gives us AC:
AC ≈ √269
AC ≈ 16.4 km
Now, we can find the angle between the north direction and the line AC. This can be done using trigonometric ratios, specifically the tangent function:
tan(θ) = opposite/adjacent
tan(θ) = BC/AB
tan(θ) = 13/10
θ ≈ arctan(13/10)
Using a calculator or an online tool to find the inverse tangent (arctan) of 13/10, we get:
θ ≈ 51.34 degrees
Therefore, the bearing of point C from point A is approximately 51.34 degrees, or you could say 51.34° west of north.
Draw a diagram!
the bearing of C from A is
360° - arctan(13/10)