An airplane flies at an altitude of 6 miles toward a point directly over an observer. Consider 𝜃 and x as shown in the figure.

Question

(a) Write 𝜃 as a function of x.

𝜃  = _____

(b) Find 𝜃 when x = 12 miles and x = 2 miles. (Enter your answers in radians rounded to two decimal places.)

x = 12 miles 𝜃 ≈ ________

x = 2 miles 𝜃 ≈ ________

Answer 1

Hello, Aerin,

The tangent of an angle is equal to the opposite/adjacent. tan(Ø) = 6/x

At 12 miles, tan(Ø) = 6/12 or 0.5

Ø = 0.55 radians

At 2 miles I get tan(Ø) = 2/12 or 1/6

Ø = 0.17 radians

Bob