Question

An airplane is flying vertically above a straight horizontal line. The angles of depression of two consecutive kilometer stones on the opposite side of the airplane are U and B. What is the distance of the airplane from the kilometer stone at an angle of depression θ?

(a) H = D * tan(U)
(b) H = D * tan(B) - D
(c) tan(θ) = H/D
(d) tan(θ) = [tan(U)]/[1 + tan(U)]
(e) tan(θ) = [tan(B) - 1]/[1 + tan(B)]

Answer 1

The distance of the airplane from the kilometer stone at an angle of depression θ can be found using the equation H = D * [tan(B) - 1]/[1 + tan(B)].

Step-by-step explanation:

In order to find the distance of the airplane from the kilometer stone at an angle of depression θ, we can use the trigonometric function tangent (tan). The correct equation is option (e) tan(θ) = [tan(B) - 1]/[1 + tan(B)].

Let's break down the equation: tan(θ) is equal to the distance from the airplane (H) divided by the distance between the airplane and the kilometer stone (D). So when we rearrange the equation, we get H = D * [tan(B) - 1]/[1 + tan(B)].

This equation gives us the correct distance.