Expert: Azeem Hussain - 9/22/2009

Question
An airplane takes off with an angle of elevation of 25º. It flies 1,100 feet before the angle levels off. What is the plane's altitude at this point?

--i just don't understand what equation i would need to use to find the answer to this problem.
there are others like this, but this would help give me an understanding

Answer
Hi Akire,

Sketch the ground.  Sketch the diagonal at 25 degrees to the ground.  Connect the diagonal to the ground.  You now have a right triangle.

A right triangle means you can do basic trigonometric operations, such as sin, cos, and tan.  You know the diagonal (1,100 feet) and you need to find the altitude.  Relative to the given angle, the relevant sides for this problem are the opposite side and the hypotenuse.  The trigonometric operator needed is sine.
sin< = opp/hyp
sin(25)=opp/(1100)
opp=1100sin(25)

The plane's altitude is exactly [1100sin(25)] feet, or approximately to 464.88 feet.

Thanks for asking,
Azeem