Question

1. after flying 400 kilometers, a pilot noticed that his course was off by 1°. how far from its original path is the plane now?

Explanation:

Step1: Set up a right - triangle model

We can consider a right - triangle where the hypotenuse is the distance the plane has flown ($d = 400$ km) and the angle between the actual path and the intended path is $\theta=1^{\circ}$. We want to find the side opposite the angle $\theta$.

Step2: Use the sine function

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 1^{\circ}$ and the hypotenuse $h = 400$ km. So, the distance $x$ from the original path (opposite side) is given by $x = h\sin\theta$.

Step3: Calculate the value

We know that $\sin(1^{\circ})\approx0.01745$ and $h = 400$ km. Then $x=400\times\sin(1^{\circ})$. Substituting the value of $\sin(1^{\circ})$, we get $x = 400\times0.01745=6.98$ km.

Answer:

$6.98$ km