An airplane flies 180 miles from point A in the direction 135° and then travels in the direction 240° for 90 miles. Approximately how far is the airplane from A? (Round your answer to the nearest whole number.)
according to my quick sketch you have to use the cosine law
x^2 = 180^2 + 90^2 - 2(180)(90)cos 75°
...
x = appr 179 miles
Where did you get the 75 degrees from
Can somebody explain where the 75 came from please?
To find the distance of the airplane from point A, we can use the concept of vectors. We need to break down the given information into its components.
First, let's consider the distance traveled in the 135° direction. To calculate the horizontal component, we multiply the distance (180 miles) by the cosine of the angle (135°). Similarly, for the vertical component, we multiply the distance by the sine of the angle.
Horizontal component = 180 miles * cos(135°)
Vertical component = 180 miles * sin(135°)
Now, let's do the same for the distance traveled in the 240° direction. The horizontal and vertical components can be obtained using the same formulas as before.
Horizontal component = 90 miles * cos(240°)
Vertical component = 90 miles * sin(240°)
To find the total horizontal and vertical components, we add together the respective components obtained from the two directions. This will give us the net displacement of the airplane from point A along the x and y axes.
Net horizontal displacement = (180 miles * cos(135°)) + (90 miles * cos(240°))
Net vertical displacement = (180 miles * sin(135°)) + (90 miles * sin(240°))
Finally, we can use these displacements to calculate the straight-line distance (also known as the resultant) from point A to the airplane using the Pythagorean theorem.
Distance from A = √(Net horizontal displacement)^2 + (Net vertical displacement)^2
Calculating the above expression will give us the approximate distance from point A to the airplane.