SOLUTION: Hi, It's word problems (again) mixed with angles. Please help: The angle of depression of an aircraft carrier from an approaching airplane is 48 degrees 22'. If the plane is

Question 168967: Hi,
It's word problems (again) mixed with angles. Please help:
The angle of depression of an aircraft carrier from an approaching airplane is 48 degrees 22'. If the plane is flying at an altitude of 1240m, find the horizontal distance to the carrier.
So I draw a triangle that has a height of 1240m |, and an angle |\ of 48 degrees, 22'.
I'm not sure if I even have the correct angle labeled. Please help.
Thank you.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
It's impossible to draw your diagram here but let's see if I can explain it.
Imagine you're in the cockpit of the plane. It is flying at a height of 1240m. Looking down, at a distance, he sees the aircraft carrier (at an angle of 48 deg 22 min).
.
This basically forms a "right triangle" and we're looking for the hypotenuse.
.
Converting 48 deg and 22 min to a decimal:
48 + 22/60 = 48.3667
.
Applying trigonometry:
sin = opposite/hypothenuse
.
Let x = distance to carrier
.
sin(48.3667) = 1240/x
xsin(48.3667) = 1240
x = 1240/sin(48.3667)
x = 1240/0.7474
x = 1659.059 meters

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