You can use the tangent ratio to find the airplane's altitude.
The altitude of the airplane in the given condition is 10,471.72 ft
What is angle of elevation?
You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
What is tangent ratio?
In a right angled triangle(triangle with one of the angles as right angle which is 90 degrees), seeing from perspective of an angle, the tangent ratio is the ratio of the side opposite to that angle and the side which is perpendicular to that opposite side.
How to find the airplane's altitude if angle of elevation is given?
Refer to the attached figure.
The altitude of the plane is the length of the line segment CE.
We have the rectangle ABDE, thus, AD = BE in terms of length.
(remember that |AB| means length of line segment AB).
Thus,
|CE| = |CB| + |BE| = |CB| + 1600 ft
Using the tangent ratio for triangle ABC from angle A, we get:
[tex]tan(A) = \dfrac{|CB|}{|AB|} = \dfrac{|CB|}{3055}\\\\tan(71) \approx 2.904 = \dfrac{|CB|}{3055}\\\\|CB| = 3055 \times 2.904 = 8.871.72 \: \rm ft[/tex]
Thus,
|CE| = |CB| + 1600 = 8871.72 + 1600 = 10,471.72 ft.
Thus,
The altitude of the airplane in the given condition is 10,471.72 ft
Learn more here about trigonometric ratios here:
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