An airplane is 120 miles north and 85 miles east of an airport. Find the bearing from the airplane to the airport (round to 1 decimal place)?
Good grief, another correctly worded question! We are on a roll!
Draw it on paper.
The bearing of the airport from the plane is the same angle West of South as the plane is East of North from the airport.
So where is the plane from the airport first
tan angle East of North = 85 /120
so plane bearing = 35.3 deg East of N
so airport from plane is 35.3 West of South
which is 180+35.3 = 215.3 deg Compass bearing clockwise from North
To find the bearing from the airplane to the airport, follow these steps:
Step 1: Draw a diagram and label the positions of the airplane and the airport. Let's assume the airplane is represented by point A, and the airport is represented by point B.
Step 2: Draw a straight line connecting points A and B.
Step 3: Use the right triangle formed by the airplane, the airport, and the horizontal line connecting them to calculate the angle.
Step 4: Use the tangent function to calculate the angle. The tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, the side opposite the angle is 120 miles (the north distance) and the side adjacent to the angle is 85 miles (the east distance). Therefore, the tangent of the angle is 120/85.
Step 5: Use the inverse tangent function (arctan) to find the angle itself. Take the arctan of the ratio calculated in the previous step. This will give you the angle in radians.
Step 6: Convert the angle from radians to degrees. Multiply the angle in radians by 180°/pi.
Step 7: Round the final answer to one decimal place.
Following these steps, the bearing from the airplane to the airport is approximately __° (round to one decimal place).
To find the bearing from the airplane to the airport, we can use trigonometry.
First, let's draw a diagram to make it easier to understand. Imagine a coordinate system where the airplane is located at point A, and the airport is at point B. The airplane is 120 miles north of the airport, which means point A is located 120 units directly above point B. Similarly, the airplane is 85 miles east of the airport, so point A is located 85 units to the right of point B.
Now, we have a right triangle with sides of 120 and 85 units. We can use the trigonometric function called tangent to find the bearing.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the angle we are interested in is the angle between the line connecting the airplane and the airport (line AB), and the horizontal axis (x-axis).
The tangent function is defined as: tan(θ) = opposite/adjacent.
To find the bearing, we need to find the angle θ. We can do this by taking the inverse tangent (also known as arctan or tan⁻¹) of the ratio of the opposite side to the adjacent side:
θ = tan⁻¹(120/85)
Using a calculator to evaluate this expression, we find that θ is approximately 55.8 degrees.
Therefore, the bearing from the airplane to the airport is 55.8 degrees (rounded to 1 decimal place).