Question

1. after 1 h, an airplane has travelled 350 km. strong winds, however, have caused the plane to be 48 km west of its planned flight path. by how many degrees is the airplane off its planned flight path?

Explanation:

Step1: Identify the triangle type

We can model this situation as a right triangle, where the hypotenuse is the distance the plane traveled (350 km), and the opposite side to the angle we want to find is the westward deviation (48 km). We'll use the sine function, since \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Apply the sine formula

Let \(\theta\) be the angle off the planned path. Then \(\sin(\theta)=\frac{48}{350}\).

Step3: Calculate the angle

First, compute \(\frac{48}{350}\approx0.1371\). Then, take the inverse sine (arcsin) of 0.1371: \(\theta=\arcsin(0.1371)\). Using a calculator, \(\theta\approx7.87^\circ\) (rounded to two decimal places).

Answer:

Approximately \(7.87^\circ\) (or more precisely, using a calculator for \(\arcsin(\frac{48}{350})\), the angle is about \(7.9^\circ\) when rounded to one decimal place)