At an altitude .....

Question

At an altitude of 3300 feet, the engine on a small plane fails. What angle of depression is needed to reach an airport runway that is 3 miles away by land? (Round your answer to the nearest tenth of a degree.)

Answer 1

form a right triangle with the vertical leg being 3300 and the horizontal leg being 3*5280=15,840

find the tangent of the angle which is the opposite over the adjacent

tan(?)=3300/15,840

tan(?)=0.2083333

now use your calculator, the table in your book, or an online arctan calculator to find the angle

from the table you get tan(11º40')=0.2065 and tan(11º50')=0.2095

if you take the average you get (0.2065+0.2095)/2=0.208 so you get tan(11º45'), or tan(11.75º)

using an arctan calculator you get tan(11º46') or tan(11.76º) approximately

answer: 11.8º to the nearest tenth