Answer:
1633.3 meters
Step-by-step explanation:
-Given the angle of depression is 31°, and the plane's height above the ground is 1400m.
-We use the Law of Sines to determine the distance between the plane and the rock.
-The angle of elevation from the rock to the plane is(corresponds to the plane's altitude):
[tex]\angle elevation=90-31\\=51\textdegree[/tex]
#Now, using Sine Law;
[tex]\frac{a}{Sin \A}=\frac{b}{Sin \ B}\\\\\\\frac{1400}{Sin \ 59}=\frac{d}{Sin \ 90}\\\\\\\\=1633.287\approx 1633.3\ m[/tex]
Hence, the direct distance between the plane and the rock is 1633.3 meters
