An airplane is at an elevation of 35,000 ft when it starts its descent at a 20 degree angle of depression. What is the air distance between the airplane and the airport in miles?

Accepted Solution

19.38 miles
This is a trigonometry problem. The angle of depression is 20 degrees and is the angle used with the trig ratio. Compared to that angle the altitude is the opposite side and the air distance is the hypotenuse. Change feet to miles by dividing 35000 by 5280 which is about 6.63 miles. opposite and hypotenuse is used in a sine function with the formula.
[tex]sin \theta = \frac{opp}{hyp} [/tex]
plug in known values
[tex]sin(20) = \frac{6.63}{x} [/tex]
Switch sin20 and x using the products property
[tex]x = \frac{6.63}{sin(20)} [/tex]
plug into a calculator to get the answer of 19.38