A PLANE FLIES 120km on a bearing of 045 and then flies 150km due east.how far east of the starting point is the plane?
(120 / 2) √2 + 150
To find how far east the plane is from the starting point, we need to calculate the component of the second leg (150km) that is in the eastward direction.
The plane first flies 120km on a bearing of 045 degrees. This means it travels northeast.
To find the eastward component of the 120km leg:
Eastward Component = Distance * Cos(Bearing)
Using the given values:
Eastward Component = 120km * Cos(45 degrees)
To calculate Cos(45 degrees), we can use the trigonometric identity:
Cos(45 degrees) = sqrt(2)/2 ≈ 0.707
Eastward Component = 120km * 0.707 ≈ 84.84km
Next, the plane flies 150km due east. This means it travels directly east, so the entire distance is in the eastward direction.
Therefore, the plane is 150km east of the starting point.
Adding the eastward component of the first leg (84.84km) to the entire distance of the second leg (150km):
Distance East of starting point = 150km + 84.84km ≈ 234.84km
Thus, the plane is approximately 234.84km east of the starting point.
To find the distance east of the starting point, we need to calculate the eastward component of the plane's total displacement.
First, let's understand the given information. The plane flies 120 km on a bearing of 045. In navigation, a bearing is typically measured clockwise from North. In this case, a bearing of 045 means the plane is flying northeast.
Let's break down the displacement of the plane into its northward (N) and eastward (E) components:
1. The northward component: To find the northward component, we can use trigonometry. A right-angled triangle can be formed with the hypotenuse as the total displacement of 120 km and the angle of 45 degrees. The northward component will be the side opposite to the angle. Using the sine function, we can calculate this component:
northward component = 120 km * sin(45°)
2. The eastward component: The plane then flies 150 km due east, so the eastward component is simply 150 km.
Now, let's calculate the eastward distance:
eastward distance = eastward component - northward component
eastward distance = 150 km - (120 km * sin(45°))
Using a calculator, let's evaluate the above expression step-by-step:
northward component = 120 km * sin(45°)
northward component ≈ 84.85 km
eastward distance = 150 km - (84.85 km)
eastward distance ≈ 65.15 km
Therefore, the plane is approximately 65.15 km east of the starting point.