Make a scale drawing to answer the question
A boy starts at A and walks 3km east of B he then walks 4km north to c find the distance and bearing of c from a
did you make the drawing? If so, you should easily recognize a 3-4-5 right triangle.
C is 5 km from A
the bearing of C from A is 90-arctan(4/3) = 37°
I don't understand it
To find the distance and bearing of point C from point A, we need to create a scale drawing. Let's assume that 1 cm on the drawing represents 1 km in real life.
1. Start by drawing point A on your paper.
2. Draw a line segment to represent the 3 km distance east to point B.
3. From point B, draw a vertical line segment that represents the 4 km distance north to point C.
4. Label point C.
Now that we have the scale drawing, we can measure the distance between points A and C:
5. Use a ruler to measure the distance between point A and point C on the drawing. Let's say it measures 5 cm.
The distance between points A and C in the actual world would be equal to the measured distance on the drawing, multiplied by the scale. Since 1 cm represents 1 km, the distance from point A to point C would be:
Distance = Measured distance on the drawing * Scale = 5 cm * 1 km/cm = 5 km
Now, let's find the bearing of point C from point A:
6. Draw a line segment connecting points A and C.
7. Measure the angle between this line and the north direction (usually represented by a vertical line) using a protractor.
The angle measured represents the bearing. Let's say we measure 60°.
Therefore, the distance of point C from point A is 5 km, and the bearing of point C from point A is 60°.
To make a scale drawing to answer this question, we will need to determine a suitable scale for the drawing. Let's assume we use a scale of 1 cm = 1 km.
Now, let's proceed to create the scale drawing step by step:
1. Draw a horizontal line to represent the east-west direction and label it as the x-axis. Choose a suitable length for the x-axis, keeping in mind the distance the boy walks east of point B i.e., 3 km. Suppose we choose a length of 6 cm for the x-axis, so each cm on the drawing will be equivalent to 1 km in reality.
2. From point A, measure and mark 3 cm to the right of point B along the x-axis. This point will represent the boy's position after walking 3 km east of B. Label it as point D.
3. Now, draw a vertical line upwards from point D to represent the north direction and label it as the y-axis. Choose a suitable length for the y-axis, considering the distance the boy walks north from point D to C i.e., 4 km. Suppose we choose a length of 8 cm for the y-axis, so each cm on the drawing will be equivalent to 1 km in reality.
4. From point D, measure and mark 4 cm above it along the y-axis. This point will represent point C, where the boy ends up after walking 4 km north of D.
5. Finally, draw a line connecting points A and C to represent the path taken by the boy. This line will form a right-angled triangle with sides of 3 cm and 4 cm, corresponding to the distances of 3 km and 4 km walked by the boy, respectively.
To calculate the actual distance and bearing of point C from point A, we can use the Pythagorean theorem and trigonometry.
1. Using the Pythagorean theorem, the actual distance is given by d = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 km.
2. To find the bearing of point C from point A, we can use trigonometry. The bearing is the angle that the line AC makes with the x-axis. We can calculate this angle using the inverse tangent function: tanθ = opposite/adjacent.
In this case, tanθ = 4/3. Taking the inverse tangent of both sides, we get θ = tan^(-1)(4/3) ≈ 53.13 degrees.
Therefore, the bearing of point C from point A is approximately 53.13 degrees.