A man walks 30 meters east, then 40 meters north. What is the angle he makes wit

A man walks 30 meters east, then 40 meters north. What is the angle he makes with the east direction? (2023)

A man walks 30 meters east, then 40 meters north. What is the angle he makes with the east direction? (2023)

Step 1: Understand the problem. A man walks 30 meters to the east and then 40 meters to the north.
Step 2: Visualize the movement. Draw a right triangle where one side (adjacent) is 30 meters (east) and the other side (opposite) is 40 meters (north).
Step 3: Identify the angle (θ) we want to find. This angle is between the east direction and the line from the starting point to the final position.
Step 4: Use the tangent function. The formula for tangent is tan(θ) = opposite/adjacent.
Step 5: Substitute the values into the formula. Here, opposite = 40 meters and adjacent = 30 meters, so tan(θ) = 40/30.
Step 6: Simplify the fraction. 40/30 can be simplified to 4/3.
Step 7: Use the inverse tangent function to find θ. Calculate θ = tan⁻¹(4/3).
Step 8: Use a calculator to find the angle. This gives θ ≈ 53.13 degrees.

Trigonometry – The use of tangent function to find angles in right triangles.
Coordinate Geometry – Understanding movement in a two-dimensional plane using directional components.