Question

Finding the Height of an Airplane An aircraft is spotted by two observers who are 1000 feet apart. As the airplane passes over the line joining them, each observer takes a

sighting of the angle of elevation to the plane, as indicated in the figure. How high is the airplane?
The plane is at a height of approximately 381.69 feet.

Answer 1

381.69 feet.

Explanation:

To find the height of the airplane, we can use the principles of trigonometry. Let's call the distance between each observer and the point directly below the airplane on the ground "x", and let's call the height of the airplane "h".

From observer A, we can see that the angle of elevation to the airplane is 60 degrees. From observer B, we can see that the angle of elevation to the airplane is 30 degrees.

Using trigonometry, we can set up the following equations:

tan(60) = h/x

tan(30) = h/(1000 - x)

Solving for h in both equations, we get:

h = x * tan(60)

h = (1000 - x) * tan(30)

Setting these two expressions equal to each other, we can solve for x:

x * tan(60) = (1000 - x) * tan(30)

x * sqrt(3) = 1000 - x/√3

x = (1000 * √3) / (1 + √3)

Plugging this value of x into either of the original equations, we can solve for h:

h = x * tan(60)

h ≈ 381.69 feet

Therefore, the height of the airplane is approximately 381.69 feet.