A plane flies S 60^ exto E for 100 ext km. How far east of its starting point is it?

The plane flies S $60^\circ$ E from point A to point B. This means it flies $60^\circ$ towards the East from the South direction. The total distance flown is $100 \text{ km}$. We can form a right-angled triangle where:

• The hypotenuse is the distance from A to B ($100 \text{ km}$).
• One leg is the distance traveled South.
• The other leg is the distance traveled East. The angle between the South line and the path AB is $60^\circ$.

We need to find "how far east of A is B". This is the length of the side opposite the $60^\circ$ angle in our right-angled triangle.

Let $d_E$ be the distance East. In a right-angled triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

In this case, $\theta = 60^\circ$, the opposite side is $d_E$, and the hypotenuse is $100 \text{ km}$.

We know that $\sin(60^\circ) = \frac{\sqrt{3}}{2}$.

Now, calculate the numerical value:

The plane is approximately $\boxed{\text{87 km}}$ east of A.