A plane is flying at an altitude of 12,000 feet and is preparing to land at a nearby airport. The angle from the airport to the plane is 17. To the nearest tenth of a foot, how far is the airport from the plane?
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To find the distance from the airport to the plane, we can use trigonometry. In this case, we are given the altitude of the plane (12,000 feet) and the angle of the line of sight from the airport to the plane (17 degrees).
The trigonometric function that relates the angle, opposite side, and adjacent side in a right triangle is the tangent function. In this case, the opposite side is the altitude of the plane, and the adjacent side is the distance from the airport to the plane.
Let's calculate the distance using the tangent function:
Tan(17 degrees) = (Opposite side) / (Adjacent side)
Tan(17 degrees) = 12000 / (Adjacent side)
To solve for the adjacent side (distance), we can rearrange the equation:
Adjacent side = 12000 / Tan(17 degrees)
Using a calculator, we find that Tan(17 degrees) ≈ 0.3057.
Therefore, the distance from the airport to the plane is:
Adjacent side = 12000 / 0.3057 ≈ 39276.3972 feet
Rounding to the nearest tenth of a foot, the distance from the airport to the plane is approximately 39276.4 feet.
To determine the distance from the airport to the plane, we can use trigonometry, specifically the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the angle formed between the altitude of the plane and the distance from the airport is 17°. The altitude of the plane is the opposite side, and we are looking for the adjacent side, which represents the distance to the airport.
Let's denote the distance to the airport as "x". We can set up the following equation:
tan(17°) = 12,000 / x
To find "x", we need to isolate it. We can do this by multiplying both sides of the equation by "x":
x * tan(17°) = 12,000
Now we can solve for "x" by dividing both sides by tan(17°):
x = 12,000 / tan(17°)
Using a calculator, we can evaluate tan(17°) ≈ 0.3088. Now, we can substitute this value into the equation:
x = 12,000 / 0.3088
Evaluating this expression, we find:
x ≈ 38,862.94 feet
Therefore, the distance from the airport to the plane is approximately 38,862.9 feet (rounded to the nearest tenth).
tan 17 ° = H / A
H = A tan 17 °
H = 12,000 * 0.30573
H = 3668.76 ft
H = 3668.8 ft
To the nearest tenth of a foot