Answer:
Let's denote the height of the plane above the middle point of the line joining the temples as \( h \).
Since the angles of depression from the plane to each temple are 60 degrees, we can use trigonometry to relate the height \( h \) to the distance between the temples.
Consider the right triangle formed by the midpoint of the line joining the temples, the plane, and one of the temples.
\[ \tan(60^\circ) = \frac{h}{\text{distance from midpoint to one temple}} \]
Since both temples are 2 km apart, the distance from the midpoint to one temple is \( \frac{2}{2} = 1 \) km.
\[ \tan(60^\circ) = \frac{h}{1} \]
Now, solve for \( h \):
\[ h = \tan(60^\circ) \]
\[ h = \sqrt{3} \, \text{km} \]
So, the height of the plane above the middle point of the line joining the temples is \( \sqrt{3} \) km.
