A plane is flying at an elevation of 30000 feet.
It is within sight of the airport and the pilot finds that the angle of depression to the airport is 18.
Find the distance between the plane and the airport.
Find the distance between a point on the ground directly below the plane and the airport.
Isn't 30,000/slantdistance=sin18?
huh?
b=a(tanB)
where a is your altitude, B is your angle of depression and b is your distance to airport.
b=30,000(tan(72))
b=92,330.51
To find the distance between the plane and the airport, we can use trigonometry. We will need to use the tangent function since we have the angle of depression.
1. Draw a diagram with the plane at an elevation of 30000 feet and the angle of depression of 18 degrees.
2. From the diagram, we can see that we have a right triangle. The side opposite the angle of depression is the height of the plane (30000 feet), and the side adjacent to the angle of depression is the distance between the plane and the airport.
3. We can use the tangent function to find the distance between the plane and the airport. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
So the tangent of 18 degrees is equal to the height of the plane divided by the distance between the plane and the airport.
tangent(18) = 30000 / (distance)
4. Rearrange the equation to solve for the distance:
distance = 30000 / tangent(18)
Use a scientific calculator to find the tangent of 18 degrees and then divide 30000 by that value to find the distance between the plane and the airport.
To find the distance between a point on the ground directly below the plane and the airport, we can use the Pythagorean theorem.
1. We know the height of the plane is 30000 feet.
2. From the diagram, we can see that we have a right triangle, with one leg being the distance between the plane and the airport.
3. The other leg of the triangle is the distance between the point on the ground directly below the plane (call it point B) and the airport.
4. The hypotenuse of the triangle is the distance between the plane and the airport, which we just calculated.
5. We can use the Pythagorean theorem to find the distance between point B and the airport. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, distance of point B to the airport = sqrt((distance between plane and airport)^2 - (height of plane)^2)
Use a calculator to find the square root of the difference of squares to determine the distance between the point on the ground directly below the plane and the airport.