A student starts from A and walks 3km east to B, she then walk 5km on a bearing 152 degree from 13 . She reaches a point c . Find the distance and bearing of C from A.

To find the distance and bearing of point C from point A, we'll break down the steps needed to reach C from A.

Step 1: Start from point A.
Step 2: Walk 3km east to point B.
Step 3: Walk 5km on a bearing of 152 degrees from point B to reach point C.

Now let's calculate the coordinates of point C first.

Given that point A is the starting point and the student walks 3km east to point B, we can assume the coordinates of point A are (0,0).

Step 1: Start from point A.
Coordinates of A = (0,0)

Step 2: Walk 3km east to point B.
Since the student walks east, the x-coordinate will increase by 3km.
Coordinates of B = (3,0)

Step 3: Walk 5km on a bearing of 152 degrees from point B to reach point C.
To find the coordinates of point C, we need to use trigonometry.

Using the given bearing, we can find the change in x and y coordinates from point B.

Change in x = distance * cos(bearing)
Change in y = distance * sin(bearing)

where distance = 5km and bearing = 152 degrees.

Change in x = 5 * cos(152)
Change in y = 5 * sin(152)

Calculating these values:
Change in x = -4.58 km (approximately)
Change in y = 3.81 km (approximately)

Now, adding the changes in x and y coordinates to the coordinates of point B, we can find the coordinates of point C.

x-coordinate of C = x-coordinate of B + change in x
y-coordinate of C = y-coordinate of B + change in y

x-coordinate of C = 3 + (-4.58) = -1.58 km (approximately)
y-coordinate of C = 0 + 3.81 = 3.81 km (approximately)

Coordinates of C ≈ (-1.58, 3.81)

To find the distance and bearing of C from A, we can use the distance formula and the bearing formula.

Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Bearing = arctan((y2 - y1) / (x2 - x1))

Where (x1, y1) = coordinates of A and (x2, y2) = coordinates of C.

Calculating the distance and bearing:
Distance = √((-1.58 - 0)^2 + (3.81 - 0)^2)
= √((-1.58)^2 + (3.81)^2)
≈ √(2.4964 + 14.5261)
≈ √16.0225
≈ 4 km (approximately)

Bearing = arctan((3.81 - 0) / (-1.58 - 0))
= arctan(3.81 / -1.58)
≈ arctan(-2.41)
≈ -67.4 degrees (approximately)

Therefore, the distance of point C from A is approximately 4 km, and the bearing of C from A is approximately -67.4 degrees.

To find the distance and bearing of point C from point A, we can use principles of trigonometry and geometry.

First, let's find the coordinates of point C. We have the following information:
- The student walked 3km east from A to B.
- From point B, she walked 5km on a bearing of 152 degrees from north.

Assuming point A is the origin (0,0), we can represent the coordinates of point B as (3,0) because it is 3km east from point A.

Now, let's determine the coordinates of point C. To do this, we need to break down the displacement of 5km at a bearing of 152 degrees into its x and y components. We can use the following formulas:

x-component = distance * sin(bearing)
y-component = distance * cos(bearing)

Using these formulas, let's calculate the x-component and y-component of the displacement from B to C:

x-component = 5km * sin(152°)
y-component = 5km * cos(152°)

Using a calculator, we can calculate these values:

x-component ≈ -3.78km
y-component ≈ 2.18km

Since point B was at (3,0), this means that the x-coordinate of point C will be 3 - 3.78 = -0.78km and the y-coordinate will be 2.18km.

Therefore, the coordinates of point C are approximately (-0.78km, 2.18km).

To find the distance between point A and point C, we can use the distance formula:

distance = sqrt((x2-x1)^2 + (y2-y1)^2)

Substituting the coordinates of A and C into the formula:

distance = sqrt((-0.78-0)^2 + (2.18-0)^2)
distance ≈ sqrt(0.61 + 4.75)
distance ≈ sqrt(5.36)
distance ≈ 2.31km

Hence, the distance of point C from point A is approximately 2.31 km.

To find the bearing of point C from point A, we can use the following formula:

bearing = arctan(y-component/x-component)

Substituting the values we calculated earlier:

bearing = arctan(2.18/-0.78)
bearing ≈ -68.08 degrees

The bearing is negative because it is measured clockwise from the positive x-axis.

Therefore, the distance of point C from point A is approximately 2.31 km, and the bearing of point C from point A is approximately -68.08 degrees.

she walks on a heading, not a bearing

(3,0)+(2.35,4.41) = (5.35,4.41)
so, the distance AC is √(5.35^2+4.41^2) = 6.93
bearing to C is E39.5°N
or, 50.5°

A Boy