Question

From an airplane at an altitude of 1400 meters, the angle of depression to a rock on the ground measures 31°. Find the direct line distance from the plane to the rock. Round to the nearest tenth of a meter.

Answer 1

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):

$\angle elevation=90-31\\=51\textdegree$

#Now, using Sine Law;

$\frac{a}{Sin \A}=\frac{b}{Sin \ B}\\\\\\\frac{1400}{Sin \ 59}=\frac{d}{Sin \ 90}\\\\\\\\=1633.287\approx 1633.3\ m$

Hence, the direct distance between the plane and the rock is 1633.3 meters