Question

An airplane is flying at an altitude of 11,000 feet. The pilot wants to make asmooth final descent to the runway at an angle of depression of 7º. Howfar from the runway should the pilot begin the descent? Round to thenearest tenth.

Answer 1

Given:

Altitude of plane = 11,000 feet

Angle of depression = 7 degrees

Let's find the how far away from the runway should the pilot begin to descend.

Let's first draw a figure that represents this situation:

Here, we are to solve for x.

Since the pilot is to make a descent to the runway, we are asked to find the horizontal distance fro

To solve for x, apply the trigonometric ratio formula for tan.

Thus, we have:

`\tan \theta=\frac{\text{opposite}}{\text{adjacent}}`

WHere:

Opposite side is the side opposite the given angle = x

Adjacent side is the side adjacent to the given angle = 11000

θ = 7 degrees

Thus, we have:

`\tan 7=(x)/(11000)`

Let's solve for x:

Multiply both sides by 11000

`\begin{gathered} 11000\tan 7=(x)/(11000)\ast11000 \\ \\ 11000(0.1227845609)=x \\ \\ 1350.6=x \end{gathered}`

x = 1350.6 ft

Therefore, the pilot should begin the descent at a distance of 1350.6 ft from the runway.

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