A plane flies 75 miles south from an airfield, and then travels 120 miles more in a different direction. By this time it bears S29degreesE of the airfield. In what direction is it heading. illustrate and solve.
My diagram shows a triangle with sides 75 and 120 and a con-contained angle of 29° adjacent to the 75 side
by sine law:
sinØ/75 = sin29°/120
sinØ = 75sin29°/120
Once you have the second angle Ø , it is easy to find the third angle and answer your question.
so the second angle is 17.46 and the third angle is 133.54. then it travels to NortEast direction, am I correct?
I am answering this from a Starbucks on my tablet and have no access to a calculator to check your answer.
To figure out the direction the plane is heading, we can use the concept of bearing. Bearing is the angle, measured in degrees, between the direction of an object or a point and a reference direction, which is typically north.
In this case, the plane starts by flying 75 miles south from the airfield. This means its initial bearing is 180 degrees, as south is directly opposite to north on the compass.
Next, the plane travels 120 miles in a different direction. The question states that by this time, the plane bears S29degreesE of the airfield. This means that the plane's bearing has changed by 29 degrees towards the east from the south.
To determine the final direction, we need to find the bearing from the reference direction (north) to the plane's new direction. Here's how we can do that:
1. Start with the initial bearing of 180 degrees (south).
2. Since the plane has turned 29 degrees towards the east, subtract 29 degrees from the initial bearing.
180 degrees - 29 degrees = 151 degrees.
Therefore, the plane is heading in the direction of S151degreesE from the airfield.
To illustrate this, imagine a compass rose where north is at the top.
- Start at the center of the compass rose and move the marker in the downward direction to represent the initial bearing of 180 degrees (south).
- Now, from this south direction, move the marker 29 degrees towards the right (east) to represent the change in bearing.
- The final position of the marker will indicate the heading of S151degreesE.
Note: It may be helpful to refer to a compass or visualize a compass rose while working through this to better understand the concept of bearings and directions.