Make a sketch
A student walks 50m on a bearing of 025 and then 200m due east. How far is she from her starting point
Cannot sketch on these posts.
To create a sketch of the situation, follow these steps:
1. Draw a horizontal line to represent the starting point.
2. Label the starting point as "A."
3. From point A, draw a line segment of 50 meters at an angle of 25 degrees north of east. Label the endpoint as "B."
4. From point B, draw a vertical line segment of 200 meters going directly upward. Label the endpoint as "C."
5. Finally, draw a line segment from point C back to the starting point A to complete the triangle.
The resulting sketch should show a triangle with side lengths of 50m, 200m, and an unknown side. The unknown side represents the distance from the student's starting point.
Note: It is essential to use a ruler to ensure accurate measurements in the sketch.
To solve this problem, we can create a sketch of the situation.
1. Start by drawing a horizontal line to represent the east-west direction.
2. Mark a point on the line to represent the starting position of the student.
3. Draw an arrow pointing in the direction of the bearing, which is 025. Remember that a bearing is measured clockwise from the north direction.
4. Using a protractor or estimating, draw a line segment from the starting point to represent the 50 meters the student walked in the given bearing.
5. From the end of the first line segment, draw another line segment in the east direction. This line should be 200 meters long since the student then walks 200 meters due east.
Now, you have a sketch that represents the student's journey. To determine how far she is from her starting point, you can use trigonometry.
1. Divide the triangle formed by the lines into two right triangles.
2. The side opposite the given bearing (025) is the hypotenuse of one of the right triangles.
3. Use trigonometry (specifically, the sine function) to find the length of the adjacent side. In this case, since the bearing is given as 025, you can find the length of the adjacent side by using sin(25°) = opposite/hypotenuse.
4. Calculate sin(25°) and multiply it by the length of the hypotenuse, which is 50 meters. This will give you the length of the adjacent side, which is the distance from the starting point to the end of the first line segment.
5. Next, add the length of the second line segment (200 meters). This will give you the total distance from the starting point to the end point.
By following these steps and using trigonometry, you can determine the distance the student is from her starting point.