Answer :
The height of the plane is about 3855 feet and the distance from the nearer end of the runway is about 13580 feet.
To find out the height of the plane and the distance of it from the nearer end of the runway, we have to use trigonometry.
Let's start by finding the height of the plane, h.
Using the angle of depression of 12.5 degrees, we can write this equation:
tan 12.5 = h/d
Where d is the distance from the nearer end of the runway. If we cross-multiply, we get:
d = h/tan 12.5
We can use the equation from the other angle of depression to eliminate the distance,
d.tan 17.0 = h/(d + 10,000)
By substituting the previous equation in for d, we get:
tan 17.0 = h/(h/tan 12.5 + 10,000)
Simplifying: tan 17.0 = h(tan 12.5)/(h/tan 12.5 + 10,000)
Multiplying both sides by h/tan 12.5 + 10,000:
tan 17.0 (h/tan 12.5 + 10,000) = h tan 12.5
Expanding the left side: distributed = h + 10,000 tan 17.0 tan 12.5
Simplifying and isolating h: h = 10,000 tan 17.0 tan 12.5/(tan 12.5 - tan 17.0) ≈ 3855 ft
Therefore, the height of the plane is about 3855 feet. To find the distance from the nearer end of the runway, we use the previous equation:d = h/tan 12.5 ≈ 13580 ft
Therefore, the distance from the nearer end of the runway is about 13580 feet.
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