Question

A plane is descending towards a runway in Chicago. The plane is flying at an altitude of 11 miles and is 193 miles from the runway, as measured from the ground. What angle will the plane's path make with the runway?

Answer 1

The plane will make an angle $3.26^{\circ}$ with the runway.

Explanation:

Given that the plane is flying at an altitude of 11 miles and is 193 miles from the runway, as measured from the ground.

We need to determine the angle that the plane will make with the runway.

From the given measurements, we can see that it is a right angled triangle. Hence, let us use the tangent formula to determine the angle.

The formula for the tangent is given by

$tan \ \theta=\frac{opp}{adj}$

Where $opp=11$ and $adj=193$

Substituting these values in the above equation, we get,

$tan \ \theta=\frac{11}{193}$

Dividing, we get,

$tan \ \theta=0.057$

Taking $tan^{-1}$ on both sides of the equation, we get,

$\theta= tan^{-1}(0.057)$

Simplifying, we have,

$\theta= 3.26^{\circ}$

Hence, the angle that the plane will make with the runway is $3.26^{\circ}$