A student start at x and travel 8km north and then 5km east .what is her final bearing form x?
Draw a diagram. It should be clear that
the bearing is θ, where tanθ = 5/8
To determine the final bearing of the student from point X, we can use trigonometry.
Step 1: Draw a diagram to visualize the movement. Place point X as the starting point.
Step 2: The student travels 8 km north from X. This means the student is now 8 km directly above X.
Step 3: From the 8 km point above X, the student travels 5 km east. This means the student moves horizontally to the right by 5 km, still remaining 8 km above X.
Step 4: Using the Pythagorean theorem, we can find the direct distance from the final position to X. The distance is calculated as √(8^2 + 5^2) = √(64 + 25) = √89 ≈ 9.43 km.
Step 5: To calculate the bearing, we use trigonometry. The tangent of the angle formed by the vertical distance and horizontal distance is given by tan(θ) = opposite/adjacent = 8/5.
Step 6: To calculate the angle θ, use the inverse tangent function (tan^(-1)): θ = tan^(-1)(8/5) ≈ 57.99 degrees.
Step 7: The final bearing can be described by the angle measured clockwise from the north direction. Since the student initially moved north, and then east, the final bearing is 90 degrees (east) + 57.99 degrees (clockwise from north) ≈ 147.99 degrees.
Therefore, the final bearing of the student from X is approximately 147.99 degrees.
To determine the final bearing from point x, we can use trigonometry. The final bearing is essentially the angle between the initial position (point x) and the final position.
In this scenario, the student travels 8km north and then 5km east. We can represent these displacements as vectors. The vector for the northward displacement is (0, 8) because there is no change in the eastward direction. Similarly, the vector for the eastward displacement is (5, 0) because there is no change in the northward direction.
To find the resultant vector, we can add these two vectors together. Adding (0, 8) and (5, 0), we get (5, 8). Now, we have the displacement vector from x to the final position.
To calculate the final bearing, we need to determine the angle that this vector makes with the reference axis (typically the positive x-axis).
Using trigonometry, the tangent of the angle θ can be calculated as the ratio of the vertical component (8) to the horizontal component (5). In this case, tan(θ) = 8/5.
To find the angle θ, we can take the inverse tangent (also known as arctan) of this ratio: θ = arctan(8/5).
Using a calculator or an online tool, we can find that arctan(8/5) is approximately 56.31 degrees.
Therefore, the student's final bearing from point x is approximately 56.31 degrees.