An airplane is flying at an altitude of 4000 ft above the ground. The pilot sights an object on the ground at an angle of depression 20 degrees. What is the slant range from the airplane to the object?
2007-06-07 13:11:30 · 3 answers · asked by Taylor 1 in Education & Reference ➔ Homework Help
I had to look up "slant range" which is the line of sight, or the hypotenuse of the right triangle formed by (in this case) the pilot, the object sighted, and the ground directly under the pilot, if we assume that the ground is flat.
Since the angle of depression is 20 degrees, the angle between the ground and the line of sight from the object to the pilot is also (alternate interior angles). Distance from pilot to ground is 4000 ft. (this is one leg of right triangle) and is side opposite the 20 degree angle.
sin 20 = 4000/hypotenuse;
multiply both sides by hypotenuse and divide by sin 20 to get
hypotenuse = 4000/sin 20 = 11695 ft.
2007-06-07 13:33:19 · answer #1 · answered by Linda O 1 · 0⤊ 0⤋
USE "SOHCAHTOA."
You're giving the opposite leg and the degree.
In order to solve for the hypotenuse which is
the slant, you must use "SOH" meaning it'd be
S = SIN.
O = Opposite.
H = Hypotenuse.
SIN = O / H.
WHICH IS:
sin20° = 4000 / x
You're solving for x.
sin20° = 4000 / x
x = 4000 / sin20°
Use a graphing calculator.
2007-06-07 13:22:40 · answer #2 · answered by lvliss.lvlanda 4 · 0⤊ 0⤋
R = 4000/sin20 = 11695.2
2007-06-07 13:21:01 · answer #3 · answered by jsardi56 7 · 0⤊ 0⤋