Pythagoras theorem states that for a right angle triangle the square of the hypotenuse is equal to the sum of the other two sides of the plane. The distance (x) from the plane (P) to the observer (O) is 22417.75 feet.
Given information-
The observer angle to the plane is 42 degrees.
The height of the plane is 15000 feet.
As angle O is 42 degree and the height is 15000. Let suppose the base is y feet long. Thus angle O can be given as,
[tex]\begin{aligned}
\tan42^o&=\dfrac{15000}{y} \\
y&=\dfrac{15000}{\tan42^o} \\
y&=16660\\
\end[/tex]
Thus the base of the right triangle is 16660 feet.
Pythagoras theorem
Pythagoras theorem states that for a right angle triangle the square of the hypotenuse is equal to the sum of the other two sides of the plane.
For the given problem the the hypotenuse side is x feet.
[tex]\begin{aligned}\\
x^2&=15000^2+16660^2\\
x&=22417.75\\
\end[/tex]
Thus the distance (x) from the plane (P) to the observer (O) is 22417.75 feet.
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