Answer: We can use trigonometry to solve this problem. Let's call the height of the airplane H, and let's call the distance from observer X to the airplane D. Then the distance from observer Y to the airplane is L - D.
From the point of view of observer X, we can write:
tan(A) = H / D
tan(25°) = H / D
From the point of view of observer Y, we can write:
tan(B) = H / (L - D)
tan(25°) = H / (L - D)
We now have two equations with two unknowns (H and D). We can solve for one of the unknowns in terms of the other, and then substitute that expression into the other equation to eliminate one of the unknowns.
Let's solve the first equation for D:
D = H / tan(25°)
Substituting this expression for D into the second equation, we get:
tan(25°) = H / (L - H / tan(25°))
Multiplying both sides by (L - H / tan(25°)), we get:
tan(25°) (L - H / tan(25°)) = H
Expanding the left-hand side, we get:
tan(25°) L - H = H tan^2(25°)
Adding H to both sides, we get:
tan(25°) L = H (1 + tan^2(25°))
Dividing both sides by (1 + tan^2(25°)), we get:
H = (tan(25°) L) / (1 + tan^2(25°))
Now we can substitute this expression for H into the equation D = H / tan(25°) to get:
D = ((tan(25°) L) / (1 + tan^2(25°))) / tan(25°)
Simplifying, we get:
D = L / (1 + tan^2(25°))
Now that we know the distance D, we can use the equation tan(A) = H / D to find H:
tan(25°) = H / D
H = D tan(25°)
Substituting D = L / (1 + tan^2(25°)), we get:
H = (L / (1 + tan^2(25°))) tan(25°)
Plugging in the given values L = 1850 feet and A = B = 25°, we get:
H = (1850 / (1 + tan^2(25°))) tan(25°)
H ≈ 697.3 feet
Therefore, the airplane is about 697.3 feet high.
Explanation: