A plane flying along a straight path loses altitude at the rate of 1000 ft for each 5200 ft covered horizontally. What is the angle of descent of the plane? (Round your answer to one decimal place.)
To find the angle of descent of the plane, we can use the definition of tangent. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the opposite side is the altitude (1000 ft) and the adjacent side is the distance covered horizontally (5200 ft).
So, the tangent of the angle of descent is given by:
Tangent(angle) = Opposite / Adjacent
Tangent(angle) = 1000 / 5200
To find the angle, we can take the inverse tangent (arctan) of this ratio:
Angle = arctan(1000/5200)
Using a calculator, we find that the angle is approximately 11.7 degrees.
Therefore, the angle of descent of the plane is approximately 11.7 degrees.