A nomacl walks 11km due North from A to B.He then walks 6.5km due east from B to C. Calculate

1.the bearing of C from A
2./AC/

#1. tanθ = 6.5/11

#2 AC^2 = 11^2 + 6.5^2

1. The bearing of C from A can be calculated using trigonometry. Since the nomacl walks 11km due North and then 6.5km due East, we can create a right-angled triangle with the hypotenuse as the line AC. The angle opposite from the 11km side is the bearing.

To find the bearing, we use the tangent function: tan(θ) = (opposite/adjacent)

tan(θ) = 6.5km/11km
θ ≈ 30.96 degrees

Therefore, the bearing of C from A is approximately 30.96 degrees.

2. To find the length of AC, we can use the Pythagorean theorem. In the right-angled triangle formed by the 11km side (AB) and the 6.5km side (BC), the hypotenuse AC is the distance between points A and C.

AC^2 = AB^2 + BC^2
AC^2 = 11km^2 + 6.5km^2
AC^2 ≈ 121km^2 + 42.25km^2
AC^2 ≈ 163.25km^2

Taking the square root of both sides, we get:
AC ≈ √(163.25km^2)
AC ≈ 12.78km

Therefore, the length of AC is approximately 12.78km.

To calculate the bearing of point C from point A, we will use trigonometry.

Let's label the angle between the north direction and the line segment AC as angle θ.

1. Bearing of C from A:
Since AB is completely directed toward the north, the angle θ will be the angle between AB and AC. We can find θ using the tangent function:

tan(θ) = (distance from B to C) / (distance from A to B)

tan(θ) = 6.5 km / 11 km
θ ≈ 0.5236 rad

To convert from radians to degrees, we multiply by 180/π:

θ ≈ 0.5236 rad * 180/π ≈ 30 degrees

Therefore, the bearing of C from A is approximately 30 degrees.

2. |AC| or the distance between point A and C:
To find the length of AC, we can use the Pythagorean theorem:

AC = √((distance from A to B)² + (distance from B to C)²)
AC = √((11 km)² + (6.5 km)²)
AC ≈ √(121 km² + 42.25 km²)
AC ≈ √(163.25 km²)
AC ≈ 12.8 km

Therefore, |AC| or the distance between point A and C is approximately 12.8 km.

To find the bearing of point C from point A, we need to calculate the angle between the line AB and the line AC.

To calculate the angle, we can use trigonometry. We have the lengths of the sides of the triangle formed by points A, B, and C. Given that AB is the adjacent side and BC is the opposite side, we can use the tangent function:

1. Calculate the bearing of C from A:
- Calculate the angle using the tangent function:
angle = arc tan(BC / AB)
- Since we have opposite and adjacent sides of a right-angled triangle, we can use the inverse tangent function (arctan) to find the angle:
angle = arctan(6.5 km / 11 km)
Use a calculator to find the angle (approximately 30.96 degrees).

- The bearing is given in angles relative to North. The bearing of point C from point A would be 30.96 degrees east of North.

2. Calculate the length of AC:
- We can use the Pythagorean theorem to find the length of the side AC.
AC^2 = AB^2 + BC^2
AC^2 = 11 km^2 + 6.5 km^2
AC^2 = 121 km^2 + 42.25 km^2
AC^2 = 163.25 km^2
AC ≈ √163.25 km
Use a calculator to find the approximate value of AC, which is approximately 12.78 km.

So, the answers to the given questions are:
1. The bearing of point C from point A is approximately 30.96 degrees east of North.
2. The length of AC is approximately 12.78 km.