Question

An airplane is flying over the town of Colonsay, between two tracking stations. The angle of elevation from Station 1 is 36º, and from Station 2 is 48°. If the stations are 1675 m apart, what is the altitude of the plane, to the nearest tenth of a metre?

Answer 1

To find the altitude of the airplane, we apply trigonometry using the tangent function with the given angles of elevation from two tracking stations and their known distance apart.

Step-by-step explanation:

To determine the altitude of the airplane flying over Colonsay, we can set up a system using trigonometry principles, specifically the tangent function, which relates the angles of elevation to the distances from the stations to the airplane.

Let's denote the altitude of the airplane as 'h'. Using Station 1 with a 36° angle of elevation, we have:

tangent(36°) = opposite/adjacent

tangent(36°) = h/x

where 'x' is the distance from Station 1 to the point on the ground directly below the airplane.

Using Station 2 with a 48° angle of elevation, we have:

tangent(48°) = h/(1675 - x)

Now we have a system of two equations:

1. tangent(36°) = h/x
2. tangent(48°) = h/(1675 - x)

To solve for 'h', we need to solve these equations simultaneously, which would typically involve algebraic manipulation. The final altitude calculation would provide the answer to the nearest tenth of a metre.